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Questions and Answers

What is the potential energy of a point particle of mass in region I?

  • Zero (correct)
  • Depends on the speed
  • Undefined
  • Non-zero

What is the direction of the impulsive force at the boundary in region II?

  • In the x-direction
  • In the positive y-direction
  • In the y-direction
  • In the negative x-direction (correct)

What is the dimension of linear momentum in the given system of units?

  • L^3
  • L^1 (correct)
  • L^0
  • L^2

What is the dimension of surface tension in the given system of units?

<p>L^1 (B)</p> Signup and view all the answers

What is the location of the point charge in the given problem?

<p>At the center of the shell (C)</p> Signup and view all the answers

What is the condition for the refractive indices of the prism when the ray emerges out at a grazing angle?

<p>$n_1\sin A = n_2\sin B$ (C)</p> Signup and view all the answers

What is the direction of the electric field inside the hollow spherical conducting shell?

<p>Radial (C)</p> Signup and view all the answers

What is the condition for the two masses to follow a closed orbit?

<p>$\frac{Gm_1m_2}{r^2} = v^2$ (D)</p> Signup and view all the answers

What is the shape of the mercury surface when the beaker is rotated?

<p>Parabolic (A)</p> Signup and view all the answers

What is the coordinate of the image formed by the mercury surface mirror?

<p>$-\frac{h}{r}$ (B)</p> Signup and view all the answers

What is the force responsible for the formation of the parabolic surface of the mercury?

<p>Centrifugal force (A)</p> Signup and view all the answers

What is the type of motion exhibited by the masses when they follow a closed orbit?

<p>Elliptical (B)</p> Signup and view all the answers

What is the type of force that causes the masses to follow a closed orbit?

<p>Gravitational (C)</p> Signup and view all the answers

What is the quantity that is conserved in the motion of the two masses?

<p>Angular momentum (C)</p> Signup and view all the answers

What is the marking scheme for a correct numerical value entered at the designated place?

<p>+3 (A)</p> Signup and view all the answers

What happens in all other cases according to the marking scheme?

<p>0 (D)</p> Signup and view all the answers

What is the shape of the arrangement described in the question stem for Question Nos. 7 and 8?

<p>Uniform hemispheres (C)</p> Signup and view all the answers

What is the location of the top half of the arrangement in the question stem for Question Nos. 7 and 8?

<p>Nailed to a support (D)</p> Signup and view all the answers

What is the situation that is being avoided in the question stem for Question Nos. 7 and 8?

<p>The bottom half falls (D)</p> Signup and view all the answers

What is the angle of the ramp in the question stem for Question Nos. 9 and 10?

<p>Unknown (A)</p> Signup and view all the answers

What is the height of the table in the question stem for Question Nos. 9 and 10?

<p>4 m (A)</p> Signup and view all the answers

What is the initial situation with the spring in the question stem for Question Nos. 9 and 10?

<p>The spring is pushed down (C)</p> Signup and view all the answers

What is the ratio of the largest and smallest volumes in the process?

<p>Compression factor (A)</p> Signup and view all the answers

What type of process does the cycle follow in the path 2?

<p>Adiabatic process (B)</p> Signup and view all the answers

What is the value of γ, the adiabatic index of air?

<p>1.67 (C)</p> Signup and view all the answers

What is the final velocity of the sphere when = 0 and =?

<p>3/10 (C)</p> Signup and view all the answers

What is the number of moles of ideal gas undergoing the process?

<p>1 mole (B)</p> Signup and view all the answers

What is the efficiency of the cycle?

<p>η (D)</p> Signup and view all the answers

What are the temperatures at points 2 and 1 respectively?

<p>T₁ and T₂ (B)</p> Signup and view all the answers

What is the correct option for the cycle?

<p>η (B)</p> Signup and view all the answers

What is the marking scheme for each question?

<p>+3 if the correct value is entered, 0 in all other cases (C)</p> Signup and view all the answers

What is the temperature coefficient of resistance of the nickel heating filament?

<p>0.0068 (C)</p> Signup and view all the answers

What is the initial temperature of the nickel heating filament?

<p>293 K (D)</p> Signup and view all the answers

What is the final temperature of the nickel heating filament?

<p>1000 K (B)</p> Signup and view all the answers

What is the surface area of the filament?

<p>Not given (B)</p> Signup and view all the answers

What is the mass of the wedge in Q.16?

<p>Not given (A)</p> Signup and view all the answers

What is the angle of the wedge in Q.16?

<p>θ (B)</p> Signup and view all the answers

What is the frequency of the tone played by the source in Q.17?

<p>400 Hz (D)</p> Signup and view all the answers

Study Notes

Physics Questions

  • A point particle of mass is in region I with potential energy = 0 and in region II with potential energy .

Dimensions of Physical Quantities

  • In a system of units, mass and torque are dimensionless, and length has a dimension of .
  • Linear momentum has a dimension of .
  • Angular momentum has a dimension of .
  • Surface tension has a dimension of .
  • Pressure has a dimension of .

Electric Charge and Conduction

  • A positive point charge is located inside a neutral hollow spherical conducting shell with inner radius and outer radius .
  • The shell is centered on the origin, and the point charge is located at the origin.

Thermodynamic Process

  • One mole of an ideal gas undergoes a process with an adiabatic index .
  • The process has a compression factor defined as the ratio of the largest and smallest volumes.
  • The efficiency of the cycle is , and the temperatures at points 2 are respective.

Mechanics

  • A small box of mass is kept on a frictionless ramp with a spring at a height from a horizontal table.
  • The ramp is angled at to the horizontal, and the spring is pushed down by compared to its rest length.
  • The box leaves the ramp at a speed and lands at a distance away from the table.

Gravitation

  • Two masses are separated by a distance and move with initial velocities in opposite directions.
  • The masses interact through universal gravitation, and the condition for them to start following a closed orbit is .

Reflection and Refraction

  • A prism with refractive indices satisfies the condition for a ray to emerge at a grazing angle.
  • The refractive indices satisfy one of the options:, , or .

Rotating Beaker of Mercury

  • A beaker of radius is filled with mercury partly up to a height and is rotated about its axis with a constant angular velocity.
  • The mercury surface attains a parabolic shape with a radius of curvature and acts as a mirror for a point object.
  • The -coordinate of the image is one of the options:,, or.

Heating Filament

  • A heater has a nickel heating filament with a temperature coefficient of resistance and a resistance at room temperature.
  • The filament becomes red-hot at a temperature due to a current passing through it.
  • The total surface area of the filament is .

Block and Wedge

  • A wedge of mass is kept at rest on a horizontal surface, and a block of mass is kept on the wedge at a height from the surface.
  • The angle of the wedge is , and there is no friction between the block and wedge or between the surface and the wedge.
  • The system is released into a free motion, and the time taken by the block to reach the horizontal surface is .

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