Monday 08th August 2022

**Q. 1.** Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I,
would be

**Sol.** Correct choice: (1)

**Q. 2.** A particle moving along x-axis has acceleration f, at time t, given

are constant. The particle
at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0 , the particle’s velocity (v_{x} ) is

**Sol.**

If they have asked instantaneous velocity when Correct choice: (1)

**Q. 3.** A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd .The average speed for this round trip is

**Sol. **In question it must be car moves from X to Y and returns to X.

Correct choice: (2)

**Q. 4. **A particle starting from the origin (0, 0) moves in a straight line in the (x, y) plane. Its co-ordinates at a later time are . The path of the particle makes with the x-axis an angle of

**Sol.** Correct choice: (4)

**Q. 5.** A block B is pushed momentarily along a horizontal surface with an initial velocity V. If is the coefficient of sliding friction between B and the surface, block B will come to rest after a time

**Sol.** Correct choice: (2)

**Q. 6.** A vertical spring with force constant K is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d . The net work done in the process is

**Sol.**

Correct choice: (3)

**Q. 7.** A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad / sec. In a time of 2 sec it has rotated through an angle (in radian) of

- 4
- 6
- 10
- 12

**Sol.** Correct choice: (3)

**Q. 8.**

**Sol.**

Correct choice: (2)

**Q. 9.** The position x of a particle with respect to time t along x -axis is given by where x is in metres and t in second. What will be the position of this particle when it achieves maximum speed along the +_{x} direction?

- 24 m
- 32 m
- 54 m
- 81 m

**Sol.** Correct choice: (3)

**Q. 10.** A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan?

- 4.0 cm
- 8.0 cm
- 10.0 cm
- any value less than 12.0 cm

**Sol.** Correct choice: (3)

**Q. 11.** A particle of mass m moves in the XY plane with a velocity V along the straight line AB. If the angular momentum of the particle with respect to origin O is L_{A} when it is at A and L_{B} when it is at B, then

- The relationship between L
_{A}and L_{B}depends upon the slope of the line AB

**Sol.** Correct choice: (3)

**Q. 12.** A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about , the initial angular acceleration of the rod will be

**Sol. ** Correct choice: (1)

**Q. 13.** Two satellites of earth, are moving in the same orbit. The mass of is four times the mass of . Which one of the following statements is true?

- The kinetic energies of the two satellites are equal.
- The time period of is four times that of .
- The potential energies of earth and satellite in the two cases are equal.
- are moving with the same speed.

**Sol .** As orbital velocity it is independent of mass of satellite Correct choice: (4)

**Q. 14.** Assuming the sun to have a spherical outer surface of radius r , radiating like a black body at temperature , the power
received by a unit surface, (normal to the incident rays) at a distance R from the center of the sun is (where is the Stefan’s constant).

**Sol. **Power radiated

Correct choice: (1)

**Q. 15.** An engine has an efficiency of 1/6. When the temperature of sink is reduced by 62^{0}C, its efficiency is doubled. Temperature of the source is

**Sol.** Correct choice: (1)

**Q. 16.** A black body is at . It emits energy at a rate which is proportional to

**Sol.** Correct choice: (3)

**Q. 17.** The frequency of a light wave in a material is and wavelength is 5000Å. The refractive index of material will be

- 1.33
- 1.40
- 1.50
- 3.00

**Sol.** Correct choice: (4)

**Q. 18.** The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

- (1) zero

**Sol.**

Correct choice: (2)

**Q. 19.** The particle executing simple harmonic motion has a kinetic energy . The maximum values of the potential energy and the total energy are respectively

**Sol.** Correct choice: (1)

**Q. 20.** A particle executes simple harmonic oscillation with an amplitude a . The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

- T / 2
- T / 4
- T / 8
- T /12

**Sol. ** Correct choice: (4)