Physics All Chapters Previous Year Board Questions PDF

## SUMMARY OF QUESTIONS ASKED IN PREVIOUS BOARD EXAMS ### 1 ROTATIONAL DYNAMICS **Theory:** 1. Derive an expression for kinetic energy, when a rigid body is rolling on a horizontal surface without slipping. Hence find kinetic energy for a solid sphere. (March 2013) 2. A particle of mass *m*, just...

## SUMMARY OF QUESTIONS ASKED IN PREVIOUS BOARD EXAMS ### 1 ROTATIONAL DYNAMICS **Theory:** 1. Derive an expression for kinetic energy, when a rigid body is rolling on a horizontal surface without slipping. Hence find kinetic energy for a solid sphere. (March 2013) 2. A particle of mass *m*, just completes the vertical circular motion. Derive the expression for the difference in tensions at the highest and the lowest points. (March 2013) 3. For a particle performing uniform circular motion **ω** = **v** × **r**, obtain an expression for linear acceleration of the particle performing non-uniform circular motion. (Feb. 2014) 4. State and prove the theorem of 'parallel axes'. (Feb. 2014, 2016, July 2023) 5. State the law of conservation of angular momentum and explain with a suitable example. (Oct. 2014, July 2022) 6. Draw a diagram showing all components of forces acting on a vehicle moving on a curved banked road. Write the necessary equation for maximum safety, speed and state the significance of each term involved in it. (Oct. 2014) 7. In circular motion, assuming **ω** = **a** × **r**, olbtain an expression for the resultant acceleration of a particle in terms of tangential and radial component. (Feb. 2015) 8. State the theorem of parallel axes and theorem of perpendicular axes about moment of inertia. (Feb. 2015) 9. State an expression for the moment of inertia of a solid uniform disc, rotating about an axis passing through its centre, perpendicular to its plane. Hence derive an expression for the moment of inertia and radius of gyration: (i) about a tangent in the plane of the disc, and (ii) about a tangent perpendicular to the plane of the disc. (Oct. 2015) 10. Draw a neat labelled diagram of conical pendulum. State the expression for its periodic time in terms of length. (Oct. 2015) 11. In U. C. M. (Uniform Circular Motion), prove the relation **a** = **v** × **ω**, where symbols have their usual meanings. (Feb. 2016) 12. Obtain an expression for total kinetic energy of a rolling body in the form 1/2 * MV² * [1+ K²/R²] (Feb. 2016) 13. Obtain an expression for torque acting on a body rotating with uniform angular acceleration. (Feb. 2016) 14. Draw a neat labelled diagram showing the various forces and their components acting on a vehicle moving along curved banked road. (July 2016, 2017) 15. Explain the concept of centripetal force. (July 2016) 16. Explain the physical significance of radius of gyration. (March 2017) 17. Define moment of inertia. State its SI unit and dimensions. (October 2008, March 2018) 18. Distinguish between centripetal force and centrifugal force. (March 2009, 2010, 2018) 19. State and prove the law of conservation of angular momentum. (March 2011, 2018, Oct. 2011, 2015, Feb. 2023) 20. Define radius of gyration. Explain its physical significance. (March 2008, 2019, July 2018) 21. What is the value of tangential acceleration in U.C.M.? (March 2019) 22. Obtain expressions of energy of a particle at different positions in the vertical circular motion. (March 2019) 23. Define U.C.M. Name the forces acting on a body executing non-uniform circular motion. (July 2019) 24. Explain the principle of conservation of angular momentum with the help of two appropriate examples. (July 2019) 25. Define uniform circular motion. (March 2020) 26. Obtain the relation between the magnitude of linear acceleration and angular acceleration in circular motion. (March 2020) 27. State and prove the principle of parallel axes in rotational motion. (March 2020) 28. State the formula for moment of inertia of solid sphere about an axis passing through its center. (Oct. 2021) 29. Define moment of inertia of a rotating rigid body. State its SI Unit and dimensions. (Oct. 2021) 30. Using the energy conservation, derive the expression for minimum speeds at different locations along a circular motion controlled by gravity. (March 2022) 31. Derive an expression for kinetic energy of a rotating body. (March 2022) 32. Derive an expression for the kinetic energy of a body rotating with a uniform angular speed. (March 2022) 33. If friction is made zero for a road, can a vehicle move safely on this road? (Feb. 2023) 34. Derive an expression for linear velocity at lowest position, midway position and the top-most position for a particle revolving in a vertical circle, if it has to just complete circular motion without string slackening at top. (Feb. 2023) 35. Define centripetal force. (Feb. 2024) 36. Derive an expression for maximum speed of a vehicle moving along a horizontal circular track. (Feb. 2024) **Problems:** 1. A car of mass 1500 kg rounds a curve of radius 250 m at 90 km/hour. Calculate the centripetal force acting on it. (March 2013) 2. A wheel of moment of inertia 1 kgm² is rotating at a speed of 40 rad/s. Due to friction on the axis, the wheel comes to rest in 10 minutes. Calculate the angular momentum of the wheel, two minutes before it comes to rest. (March 2013) 3. A ballet dancer spins about a vertical axis at 2.5n rad/sec. with his both arms outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by 25%. Calculate the new rotation in r.p.m. (Oct 2013) 4. A racing car completes 5 rounds on a circular track in 2 minutes. Find the radius of the track if the car has uniform centripetal acceleration of n² m/s². (Oct 2013) 5. In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a vertical axis, calculate tension in the string (g = 9.8 m/s²) (Oct 2013) 6. A stone of mass 1 kg is whirled in horizontal circle attached at the end of a 1 m long string. If the string makes an angle of 300 with vertical, calculate the centripetal force acting on the stone. (g = 9.8 m/s²). (Feb. 2014) 7. A solid cylinder of uniform density of radius 2 cm has mass of 50 g. If its length is 12 cm, calculate its moment of inertia about an axis passing through its centre and perpendicular to its length. (Feb. 2014) 8. A body starts rotating from rest. Due to a couple of 20 Nm it completes 60 revolutions in one minute. Find the moment of inertia of the body. (Oct. 2014) 9. A stone of mass 5 kg, tied to one end of a rope of length 0.8 m, is whirled in a vertical circle. Find the minimum velocity at the highest point and at the midway point. [g = 9.8 m/s²] (Oct 2014) 10. The spin dryer of a washing machine rotating at 15 r.p.s. slows down to 5 r.p.s. after making 50 revolutions. Find its angular acceleration. (Feb. 2015) 11. A horizontal disc is freely rotating about a transverse axis passing through its centre at the rate of 100 revolutions per minute. A 20 gram blob of wax falls on the disc and sticks to the disc at a distance of 5 cm from its axis. Moment of inertia of the disc about its axis passing through its centre of mass is 2 x 104 kg m². Calculate the new frequency of rotation of the disc. (Feb. 2015) 12. A stone of mass 100 g attached to a string of length 50 cm is whirled in a vertical circle by giving velocity at lowest point as 7 m/s. Find the velocity at the highest point. [Acceleration due to gravity = 9.8 m/s²]. (Oct. 2015) 13. A coin kept at a distance of 5 cm from the centre of a turntable of radius 1.5 m just begins to slip when the turntable rotates at a speed of 90 r.p.m. Calculate the coefficient of static friction between the coin and the turntable. (g = 9.8 m/s²]. (Feb. 2016) 14. A stone of mass 2 kg is whirled in a horizontal circle attached at the end of 1.5 m long string. If the string makes an angle of 30° with vertical, compute its period. (g=9.8 m/s²) (July 2016) 15. A uniform solid sphere has a radius 0.1 m and density 6 × 103 kg/m³. Find its moment of inertia about a tangent to its surface. (July 2016) 16. A solid sphere of mass 1 kg rolls on a table with linear speed 2 m/s, find its total kinetic energy. (March 2017) 17. A vehicle is moving on a circular track whose surface is inclined towards the horizontal at an angle of 10°. The maximum velocity with which it can move safely is 36 km/hr. Calculate the length of the circular track. [π = 3.142] (March 2017) 18. A small body of a mass 0.3 kg oscillates in vertical plane with the help of a string 0.5 m long with a constant speed of 2 m/s. It makes an angle of 60° with the vertical. Calculate tension in the string. (g = 9.8 m/s²) (July 2017) 19. A uniform solid sphere has radius 0.2 m and density 8 x 103 kg m³. Find the moment of inertia about the tangent to its surface. (π = 3.142) (July 2017) 20. A flat curve on a highway has a radius of curvature 400 m. A car goes around a curve at a speed of 32 m/s. What is the minimum value of coefficient of friction that will prevent the car from sliding? (g = 9.8 m/s²) (March 2018) 21. The frequency of revolution of a particle performing circular motion changes from 60 r.p.m to 180 r.p.m. in 20 seconds. Calculate the angular acceleration of the particle. (π = 3.142) (July 2018) 22. A meter gauge train is moving at 72 km/hr along a curved railway of radius of curvature 500 m at a certain place. Find the elevation of outer rail above the inner rail so that there is no side pressure on the rail. (g = 9.8 m/s²) (July 2018) 23. A solid sphere of diameter 50 cm and mass 25 kg rotates about an axis through its centre. Calculate its moment of inertia. If its angular velocity changes from 2 rad/s to 1 rad/s in 5 seconds, calculate the torque applied.(July 2018) 24. A wheel of moment of inertia 1 kg m² is rotating at a speed of 30 rad/s. Due to friction on the axis, it comes to rest in 10 minutes. Calculate the average torque of the friction. (March 2019) 25. The radius of gyration of a body about an axis, at a distance of 0.4 m from its centre of mass is 0.5 m. Find its radius of gyration about a parallel axis passing through its centre of mass. (March 2019) 26. A car rounds a curve of radius 625 m with a speed of 45 m/s. What is the minimum value of coefficient of friction which prevents the car from sliding? (July 2019) 27. Find the frequency of revolution of a round disco stage revolving with an angular speed of 300 degree/second. (July 2019) 28. Energy of 1000 J is spent to increase the angular speed of a wheel from 20 rad/s to 30 rad/s. Calculate the moment of inertia of the wheel. (March 2020) 29. In a circus, a motor-cyclist having mass of 50 kg moves in a spherical cage of radius 3m. Calculate the last velocity with which he must pass the highest point without losing contact. Also calculate his angular speed at the highest point. (March 2020) 30. A motor cyclist (to be treated as a point mass) is to undertake horizontal circles inside the cylindrical wall of a well of inner radius 4 m. The co-efficient of static friction between tyres and the wall is 0.2. Calculate the minimum speed and period necessary to perform this stunt. (Oct. 2021) 31. Calculate the moment of inertia of a uniform disc of mass 10 kg and radius 60 cm about an axis perpendicular to its length and passing through its centre. (March 2022) 32 The surface density of a uniform disc of radius 10 cm is 2 kg/m². Find its M.I. about an axis passing through its centre and perpendicular to its plane. (July 2022) 33. A motorcyclist performs stunt along the cylindrical wall of a 'Well of Death' of inner radius 4 m. Coefficient of static friction between tyres and the wall is 0.4. Calculate the maximum period of revolution. (Use g = 10 m/s²) (July 2023) 34. The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/sec. (Feb 2024) ### 2 MECHANICAL PROPERTIES OF FLUIDS **Theory** 1. Derive the relation between surface tension and surface energy per unit area. (March 2013) 2. Show that the surface tension of a liquid is numerically equal to the surface energy per unit area. (Oct 2013) 3. Explain the rise of liquid in the capillary on the basis of pressure difference. (Feb 2014) 4. Define angle of contact. State its any two characteristics. (Oct. 2011, 2014, July 2022) 5. Derive an expression for excess pressure inside a drop of liquid. (Feb. 2015) 6. Draw a neat labelled diagram showing forces acting on the meniscus of water in a capillary tube. (Oct. 2015) 7. Derive Laplace's law for spherical membrane of bubble due to surface tension. (Feb. 2016, March 2018) 8. Draw a neat diagram for the rise of liquid in a capillary tube showing the components of a surface tension (March 2010, July 2016) 9. Draw a neat labelled diagram for a liquid surface in contact with a solid, when the angle of contact is acute. (March 2017) 10. Define surface tension and surface energy. (July 2017) 11. What is capillarity? State any two uses of capillarity. (October 2010, March 2011, July 2018, 2022) 12. Define angle of contract. (March 2019) 13. Obtain an expression for the rise of a liquid in a capillary tube. (July 2019) 14. On the basis of molecular theory explain the phenomenon of surface tension. (Oct. 2021) 15. Explain surface tension on the basis of molecular theory. (Oct. 2021) 16. State the formula for critical velocity in terms of Reynold's number for a flow of a fluid. (March 2022) 17. Derive an expression for terminal velocity of a spherical object falling under gravity through a viscous medium. (March 2022) 18. Define coefficient of viscosity. State its formula and S.I. units. (Feb 2023) 19. Obtain the relation between surface energy and surface tension. (Feb. 2023) 20. Distinguish between streamline flow and turbulent flow. (Any two points) (July 2023) 21. Why a detergent powder is mixed with water to wash clothes? (Feb 2024) 22. Define surface energy of the liquid. Obtain the relation between the surface energy and surface tension. (Feb. 2024) **Problems:** 1. The surface tension of water at 0°C is 75.5 dyne/cm. Find surface tension of water at 25°C. [la for water 0.0021/°C] (March 2013, 2015) 2. A soap bubble of radius 12 cm is blown. Surface tension of soap solution is 30 dyne/cm. Calculate the work done in blowing the soap bubble. (Oct 2013) 3. Calculate the density of paraffin oil, if glass capillary of diameter 0.25 mm dipped in paraffin oil of surface tension 0.0245 N/m rises to a height of 4 cm. (Angle of contact of paraffin with glass = 28º and acceleration due to gravity = 9.8 m/s².) (Feb. 2014) 4. Water rises to a height 3.2 cm in a glass capillary tube. Find the height to which the same water will rise in another glass capillary having half area of cross section. (Oct. 2014) 5. A raindrop of diameter 4 mm is about to fall on the ground. Calculate the pressure inside the raindrop. [Surface tension of water T = 0.072 N/m, atmospheric pressure = 1.013 × 105 N/m²] (Oct. 2015) 6. The energy of the free surface of a liquid drop is 5t times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system. (Feb. 2016) 7. The total free surface energy of a liquid drop is π√2 times the surface tension of the liquid. Calculate the diameter of the drop in S.I. unit. (July 2016) 8. The total energy of free surface of a liquid drop is 2n times the surface tension of the liquid. What is the diameter of the drop? [Assume all terms in SI unit). (March 2017) 9. Two soap bubbles have radii in the ratio 4:3. What is the ratio of work done to blow these bubbles? (July 2017) 10. Calculate the work done in increasing the radius of a soap bubble in air from 1 cm to 2 cm. The surface tension of soap solution is 30 dyne/cm. (π = 3.142) (March 2018) 11. A horizontal circular loop of a wire of radius 0.02 m is lowered into crude oil and a film is formed. The force due to the surface tension of the liquid is 0.0113 N. Calculate the surface tension of the crude oil. (π = 3.142) (July 2018) 12. A rod of length 4 cm is movable on a rectangular frame of wire. A film is formed in the frame. A force of 3.2 x 10-3 N is applied to the rod for its equilibrium. Find the surface tension of the liquid. (July 2019) 13. Calculate the work done in blowing a soap bubble of radius 0.1 m. (Surface tension of soap solution = 30 dyne/cm) (July 2019) 14. Compare the amount of work done in blowing two soap bubbles of radii in the ratio 4: 5. (March 2020) 15. Eight droplets of water each of radius 0.2 mm coalesce into a single drop. Fine the decrease in the surface area. (Oct. 2021) 16. Find the difference of pressure between inside and outside of a spherical water drop of radius 2 mm, if surface tension of water is 73 x 10-3 N/m. (March 2022) 17. Calculate the work done in blowing a soap bubble to a radius of 1 cm. The surface tension of a soap solution is 2.5 x 10-2 N/m. (July 2022) 18. Calculate the diameter of a water drop, if the excess pressure inside the drop is 80 N/m². (Surface Tension of water = 7.2 x 10-2 N/m) (Feb. 2023) 19. Calculate the terminal velocity with which an air bubble of diameter 0.4 mm rise through a liquid of viscosity 0.1 Ns / m² and density 900 kg/m³. Density of air is 1.29 kg/m³. (July 2023) 20. A horizontal force of 0.5 N is required to move a metal plate of area 10-2 m² with a velocity of 3 x 10-2 m/s, when it rests on 0.5 x 10-3 m thick layer of glycerin. Find the coefficient of viscosity of glycerin. (Feb. 2024) ### 3 KINETIC THEORY OF GASES AND RADIATION **Theory:** 1. Draw a neat labelled diagram for Ferry's perfectly black body. (March 2013, July 2018; Feb. 2024) 2. Explain black body radiation spectrum in terms of wavelength. (Oct 2013) 3. Show that R.M.S. velocity of gas molecules is directly proportional to square root of its absolute temperature. (Feb. 2014, March 2017) 4. Show graphically spectrum of energy distribution of black body in terms of wavelengths. (Oct. 2008, 2009, Feb. 2014) 5. Explain Maxwell distribution of molecular speed with necessary graph. (Oct 2014) 6. With a neat and labelled diagram, explain Ferry's perfectly black body. (Oct 2014) 7. State: (a) Wein's displacement law and (b) First law of thermodynamics. (Feb. 2015) 8. Define 'emissive power' and 'coefficient of emission of a body'. (Feb. 2016) 9. State Kirchhoff's law of radiation and prove it theoretically. (March 2012, July 2017, 2019) 10. What is perfectly black body? Explain Ferry's black body. (March 2019) 11. State Boyle's law. On the basis of kinetic theory of gases, obtain an expression for kinetic energy per unit volume of gas. (July 2019) 12. Explain energy distribution spectrum of a black body radiation in terms of wavelength. (March 2020) 13. Draw a neat, labelled diagram of Ferry's black body. (Oct. 2021) 14. State: (a) Stefan - Baltzmann law radiation. (b) Wien's displacement law. (Oct. 2021) 15. Derive an expression for a pressure exerted by a gas on the basis of kinetic theory of gases. (March 2022; Feb. 2023) 16. Define: (i) Emissive power (ii) Co-efficient of emission (July 2022) 17. Explain construction and working of Ferry's Black Body. (July 2023) 18. Prove the Mayer's relation: Cp - C₁ = R/J (Feb. 2024) **Problems:** 1. Calculate the kinetic energy of 10 gram of Argon molecules at 127°C. (Universal gas constant R = 8320 J/k mole K, Atomic weight of Argon = 40) (March 2013) 2. The kinetic energy of nitrogen per unit mass at 300 K is 2.5 × 106 J/kg. Find the kinetic energy of 4 kg oxygen at 600 K. (Molecular weight of nitrogen = 28, Molecular weight of oxygen = 32) (Oct 2013) 3. Calculate the average molecular kinetic energy: (a) per kilomole (b) per kilogram of oxygen at 27°C. [R = 8320 J/kmole K, Avogadros number = 6.03 × 1026 molecules/K mole] (Feb. 2015) 4. A pinhole is made in a hollow sphere of radius 5 cm whose inner wall is at temperature 727°C. Find the power radiated per unit area. (Stefan's constant o = 5.7 × 10-8 J/m²sK¹, emissivity (e) = 0.2) (Oct. 2015) 5. Compute the temperature at which the r.m.s. speed of nitrogen molecules is 832 m/s. [Universal gas constant, R = 8320 J/k mole K, molecular weight of nitrogen = 28.] (Oct. 2015) 6. A metal sphere cools at the rate of 4°C / min. when its temperature is 50°C. Find its rate of cooling at 45° C if the temperature of surrounding is 25° С. (Feb. 2016) 7. A body cools from 62°C to 54°C in 10 minutes and 48°C in next 10 minutes. Find the temperature of the surroundings. (July. 2016) 8. A body cools at the rate of 0.5°C/min. when it is 25°C above the surroundings. Calculate the rate of cooling when it is 15°C above the same surroundings. (March 2017) 9. At what temperature will average kinetic energy of gas be exactly half of its value at N.T.P.? (July 2017) 10. A body cools from 80°C to 70°C in 5 minutes and to 62°C in the next 5 minutes. Calculate the temperature of the surroundings. (Feb. 2018) 11. Compare the rates of loss of heat by a black body at 627°C and 327°C, if the temperature of surrounding is 27° C (July 2018) 12. The difference between two molar specific heats of a gas is 6000 J/kg. K. If the ratio of specific heats is 1.4 calculate the molar specific heat at constant volume. (Oct. 2021) 13. The difference between the two molar specific heats of a gas is 9000 J/kg K. If the ratio of the two specific is 1.5, calculate the two molar specific heats. (March 2022) 14. Calculate the energy radiated in half a minute by a black body of surface area 200 cm² at 127°C. (July 2022) 15. Compare the rate of loss of heat from a metal sphere at 827°C with rate of loss of heat from the same at 427° C, if the temperature of surrounding is 27°C. (Feb. 2023) 16. A 60 W filament lamp loses all its energy by radiation from its surface. The emissivity of the filament surface is 0.5 and the surface area is 5 x 10-5 m². Calculate the temperature of the filament. (Given: σ = 5.67 x 10-8 Jm-2 s¹ K-4) 17. Compare the rms speed of hydrogen molecules at 227°C with rms speed of oxygen molecule at 127°C. Given that molecular masses of hydrogen and oxygen are 2 and 32 respectively. (Feb. 2024) ### 4 THERMODYNAMICS **Theory:** 1. State first law of thermodynamics. (Feb. 2015) 2. What is isothermal process? (March 2020, Oct. 2021) 3. Write a note on free expansion in thermodynamic process. (Oct 2021) 4. What is a thermodynamic process? Give any two types of it. (March 2022) 5. What are mechanical equilibrium and thermal equilibrium? (March 2022) 6. In which thermodynamic process the total internal energy of system remains constant? (July 2022) 7. State zeroth law of thermodynamics. What are the limitations of first law of thermodynamics. (July 2022) 8. Derive an expression for the work done during an isothermal process. (Feb 2023) 9. Draw a p-V diagram and explain the concept of positive work done and negative work done. (July 2023) 10. Define: (i) Isothermal process (ii) Adiabatic process. (July 2023) 11. What is surroundings in thermodynamics? (Feb. 2024) 12. Explain the change in internal energy of a thermodynamic system (the gas) by heating it. (Feb. 2024) 13. What is isothermal process? Obtain an expression for work done by a gas in an isothermal process. (Feb. 2024) **Problems:** 1. 0.5 mole of gas at temperature 450 K expands isothermally from an initial volume of 3L to final volume of 9L. (a) What is the work done by the gas? (R = 8.319 J mol-1 K-1) (b) How much heat is supplied to the gas? (Oct 2021) 2. The initial pressure and volume of a gas enclosed in a cylinder are 2 x 105 N/m² and 6 x 10-3 m³ respectively. If work done in compressing the gas at constant pressure is 150 J, find the final volume of the gas. (March 2022) 3. An automobile engine develops 62.84 kW while rotating at a speed of 1200 rpm. What torque does it deliver? (July 2022) 4. A system releases 125 kJ of heat while 104 kJ of work is done on the system. Calculate the change in internal energy of the gas. (July 2022) 5. 104 J of work is done on certain volume of a gas. If the gas releases 125 kJ of heat, calculate the change in internal energy of the gas. (Feb. 2023) 6. An ideal mono-atomic gas is adiabatically compressed so that its final temperature is twice its initial temperature . Calculate the ratio of final pressure to its initial pressure. (Feb. 2023) 7. One mole of an ideal gas is enclosed in an ideal cylinder at 1.0 MPa and 27° C. The gas is allowed to expand till its volume is doubled. Calculate the work done if the expansion is isobaric. (July 2023) ### 5 OSCILLATIONS **Theory:** 1. Represent graphically the displacement, velocity and acceleration against time for a particle performing linear S.H.M., when it starts from the mean position. (March 2008, 2013, Oct. 2010) 2. Define an ideal simple pendulum. Show that the motion of a simple pendulum under certain conditions is simple harmonic. Obtain an expression for its period. (March 2010, 2013, July 2018) 3. Derive an expression for the period of motion of a simple pendulum. On which factors does it depend? (Oct 2013) 4. State an expression for K.E. (kinetic energy) and P. E. (potential energy) at displacement 'x' for a particle performing linear S.H.M. Represent them graphically. Find the displacement at which K. E. is equal to P. E. (Feb. 2014) 5. Define phase of S.H.M. Show variation of displacement, velocity and acceleration with phase for a particle performing linear S.H.M. graphically, when it starts from extreme position. (Oct. 2014) 6. Obtain an expression for potential energy of a particle performing simple harmonic motion. Hence evaluate the potential energy, (a) at mean position and (b) at extreme position. (Feb. 2015, March 2019) 7. Discuss the composition of two S.H.M.s along the same path having same period. Find the resultant amplitude and initial phase. (Oct. 2015) 8. Define linear S.H.M. Show that S.H.M. is a projection of U.C.M. on any diameter. (Feb. 2016) 9. Define practical simple pendulum.Show that motion of bob of pendulum with small amplitude is linear S.H.M. Hence obtain an expression for its period. What are the factors on which its period depends? (July 2016) 10. Obtain the differential equation of linear simple harmonic motion. (March 2017; Feb. 2024) 11. Prove the law of conservation of energy for a particle performing simple harmonic motion. Hence graphically show the variation of kinetic energy and potential energy w. r. t. instantaneous displacement. (March 2017) 12. Define linear simple harmonic motion. Assuming the expression for displacement of a particle starting from extreme position, explain graphically the variation of velocity and acceleration w.r.t. time. (July 2016) 13. State the differential equation of linear simple harmonic motion. Hence obtain the expression for acceleration, velocity and displacement