Physics Chapter on Vectors and Forces

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Questions and Answers

The standard used for the specification of a physical quantity is called what?

Unit

If two vectors A and B are in the same direction, then the magnitude of their resultant, R, is equal to what?

A + B

In the case of Earth revolving around the Sun, the centripetal force for circular motion is provided by what?

The gravitational force of the sun

What is the moment of inertia of a thin uniform rod of length l and mass M, about an axis passing through its center and perpendicular to its length?

Ml²/12 Signup and view all the answers

Name a solid lubricant which is used in very heavy machinery.

Graphite Signup and view all the answers

Which is the prominent mode of heat transfer in solids?

Conduction Signup and view all the answers

The deformation of the shape of an object without changing its volume is called what?

Strain Signup and view all the answers

The extra energy possessed by the surface layer of a liquid is called what?

Surface tension Signup and view all the answers

What is the SI unit of coefficient of viscosity?

Pascal-second (Pa.s) Signup and view all the answers

State parallelogram law of vector addition. Draw a diagram to illustrate the parallelogram law.

If two vectors acting on a particle at the same time be represented in magnitude and direction by the two adjacent sides of a parallelogram, their resultant vector is represented in magnitude and direction by the diagonal of the parallelogram drawn from the same point. Signup and view all the answers

Calculate the angular velocity of the second hand of a watch.

π/30 rad/s Signup and view all the answers

Calculate the power of a drilling machine if it uses 3000 J of energy in 10 seconds?

300 W Signup and view all the answers

Write one example each for the following energy transformations: (a) Conversion of kinetic energy into potential energy (b) Conversion of light energy into electrical energy (c) Conversion of electrical energy into sound energy

(a) A ball thrown vertically upwards has kinetic energy at the beginning and potential energy when it reaches the maximum height. (b) Solar panels convert light energy into electrical energy. (c) A loudspeaker converts electrical energy into sound energy. Signup and view all the answers

Explain the causes of friction.

Friction arises due to the interlocking of irregularities between the surfaces in contact. Friction can also be caused by electrostatic forces of attraction between the molecules of the two surfaces in contact. Friction arises due to the adhesion of molecules of two surfaces in contact. Signup and view all the answers

Define power. Write the SI unit of power and how it is related to horse power?

Power is the rate at which work is done. The SI unit of power is watt (W). One horsepower (hp) is equivalent to 746 watts. Signup and view all the answers

Differentiate between heat and temperature.

Heat is the total kinetic energy of the molecules of a system, while temperature is a measure of the average kinetic energy of the molecules in the system. Heat is a form of energy, while temperature is a measure of the degree of hotness or coldness. Signup and view all the answers

State Hooke’s Law. Write the SI unit of elastic modulus.

Hooke's Law states that the stress is proportional to the strain within the elastic limit. The SI unit of elastic modulus is Pascal (Pa). Signup and view all the answers

What is capillarity and how it is related to angle of contact?

Capillarity is the phenomenon of rise or fall of a liquid in a capillary tube, due to the surface tension of the liquid. The angle of contact is the angle between the tangent to the liquid surface at the point of contact with the solid surface and the tangent to the solid surface. Signup and view all the answers

The radius of a pipe decreases from 6 cm to 4 cm. If the velocity at the wider portion is 5 m/s, calculate the velocity in the narrow portion.

11.25 m/s Signup and view all the answers

Explain a variety of errors associated with the measurement of physical quantities.

Systematic errors are repeatable errors that can be traced to a specific cause, such as a faulty instrument or a bias in the measurement technique. Random errors are unpredictable errors that vary from measurement to measurement. They can be reduced by taking multiple measurements and averaging the results. Least count error is the smallest value that can be measured by a measuring instrument. It represents the inherent precision of the instrument. Absolute error is the difference between the true value of a quantity and the measured value. It is influenced by systematic, random, and least count errors. Signup and view all the answers

Explain the recoil of a gun. A bullet of mass 30 g is fired from a 6 kg gun with a velocity of 300 m/s. Find the recoil velocity of the gun.

-1.5 m/s Signup and view all the answers

(a) Derive the relation between linear velocity and angular velocity. (b) Define angular acceleration. Derive the relation between linear acceleration and angular acceleration.

(a) v = rω (b) Angular acceleration is the rate of change of angular velocity. α = (ω2 - ω1)/t. Signup and view all the answers

Write a note on the moment of inertia and radius of gyration of a rotating rigid body.

The moment of inertia of a rigid body is a measure of its resistance to rotational motion. It depends on the mass distribution of the body and the axis of rotation. The radius of gyration is the distance from the axis of rotation to a point where the entire mass of the body can be assumed to be concentrated to give the same moment of inertia. Signup and view all the answers

Explain the resolution of a vector with a diagram. Discuss one real-life example of the resolution of vectors.

Resolving a vector means breaking it down into two or more component vectors. It can be visualized using a parallelogram or a right-angled triangle. Example: A vehicle traveling on a slanted road can be considered as having two components of velocity, one along the horizontal direction and another along the vertical direction. Signup and view all the answers

Explain why the outer edge of the road is raised above the inner edge of the road at curves. Derive the expression for the angle of banking.

The outer edge of the road is raised to provide the necessary centripetal force for vehicles to negotiate the curve. The angle of banking is calculated as tanθ = v²/rg where v is the speed of the vehicle, r is the radius of the curve, and g is the acceleration due to gravity. Signup and view all the answers

State the law of conservation of energy and prove it in the case of a freely falling body.

The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In the case of a freely falling body, the potential energy at the initial position is converted into kinetic energy as it falls due to gravity. The total energy (potential + kinetic) remains constant throughout the fall. The law of conservation of energy is a fundamental principle in physics, applicable to various systems and processes. Signup and view all the answers

Write a note on heat transfer by convection and radiation.

Convection involves the transfer of heat through the movement of fluids (liquids or gases). Radiation is the transfer of heat through electromagnetic waves. Both processes are prevalent in various natural and engineered systems. Signup and view all the answers

Discuss the elastic modulus related to length elasticity. A metal wire of length 4 m and radius 1 mm is stretched by a load of 8 kg at one end and keeping the other end fixed to a ceiling. Find the extension produced if Young's modulus of the material of the wire is 9 x 10^10 N/m².

0.11 mm Signup and view all the answers

Explain the idea of surface tension and discuss an application of surface tension.

Surface tension is the tendency of a liquid surface to contract to the smallest possible area. One application of surface tension is the use of detergents, which reduce surface tension allowing cleaning liquids to penetrate fabrics and remove dirt. Signup and view all the answers

Discuss the working of (a) mercury thermometer and (b) pyrometer.

(a) Mercury thermometers work on the principle of thermal expansion of mercury. As temperature rises, mercury expands and rises in a calibrated glass tube. (b) A pyrometer is a device that measures temperature without physical contact, using infrared radiation emitted by the object. Signup and view all the answers

Derive the equation of continuity for a fluid flowing through a pipe of varying cross section. Explain the principle of continuity with an example.

The equation of continuity for an incompressible fluid is A1v1 = A2v2, where A is the cross-sectional area of the pipe and v is the velocity of the fluid. This equation states that the volume flow rate of an incompressible fluid remains constant even when the cross-sectional area changes. For example, in a pipe with a narrow section, the velocity of the fluid will increase to maintain a constant volume flow rate. Signup and view all the answers

Study Notes

Part A

The standard used for specifying a physical quantity is called a unit.
If two vectors (A and B) are in the same direction, the magnitude of their resultant (R) is A + B.
In the Earth-Sun system, the centripetal force for circular motion is provided by gravity.
The moment of inertia of a uniform rod with length (l) and mass (M), about an axis through its center perpendicular to its length, is (1/12)Ml².
A solid lubricant used in heavy machinery is graphite.
The prominent mode of heat transfer in solids is conduction.
Deformation of an object's shape without changing its volume is called shear deformation.
The extra energy possessed by the surface layer of a liquid is called surface energy.
The SI unit of viscosity coefficient is Pascal-second (Pa·s).

Part B

Parallelogram law of vector addition states that if two vectors are represented by two adjacent sides of a parallelogram, the resultant is represented by the diagonal of the parallelogram.
The angular velocity of a second hand of a clock is 0.105 radians/second.
The power of a drilling machine is calculated by dividing the energy (3000 J) by the time (10 seconds), which results in a power of 300 watts.
Examples of energy transformations can include: (a) Kinetic to potential energy (e.g., a ball falling), (b) Light to Electrical energy (e.g., solar cells), and (c) Electrical to Sound energy (e.g., a speaker).
Friction is caused by the contact between two surfaces and the resulting force opposing motion.
Power is the rate at which work is done, measured in Watts (W). Horsepower (hp) is a unit of power.
Heat is thermal energy, while temperature is a measure of the average kinetic energy of particles in a substance.
Hooke's Law states that stress is proportional to strain within the elastic limit of a material. The SI unit of elastic modulus is Pascal (Pa).
Capillarity is the tendency of a liquid to rise or fall in a narrow tube. The angle of contact determines the capillarity effect.
If the velocity at a wider portion of a pipe is 5 m/s, and the radius decreases, the velocity in the narrower portion increases.

Part C

Errors in measurement can arise from systematic errors (e.g., instrument calibration) or random errors (e.g., human observation).
The recoil of a gun is caused by the conservation of momentum where the momentum of the bullet and gun after firing must be zero. Calculation provided in text for recoil velocity of the gun.
Linear velocity (v) and angular velocity (ω) are related by v = rω, where r is the radius. Angular acceleration (α) is related to linear acceleration (a) by a = rα.
Moment of inertia (I) and radius of gyration (k) are properties of a rotating body, and I = mk².
Vectors can be resolved into components at right angles. This is used in various applications (e.g., resolving forces acting on an inclined body)
The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. In a freely falling body, the transformation occurs from potential to kinetic energy.
Conduction, convection, and radiation are different modes of heat transfer.
Young's modulus (Y) is a measure of a material’s stiffness in terms of resisting tensile stress.
Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible.
Mercury thermometers and pyrometers are instruments for measuring temperature.
The principle of continuity states that the product of the cross-sectional area and the velocity of a fluid flowing through a pipe is constant.

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Test your understanding of key concepts in physics, including units, vector addition, and forces. This quiz covers essential principles such as centripetal force, moment of inertia, and heat transfer. Challenge your knowledge with questions on physical quantities and properties of materials.