May, 2022Flame Institute

42. Two discs of the same material and thickness have radii 0.2 m and 0.6 m. Their moments of inertia about their axes will be in the ratio

(a) 1 : 81 (b) 1 : 27 (c) 1 : 9 (d) 1 : 3 Ans. a (16)

3. The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in time interval from zero to 8 second will be

Ans. d (17)

The moment of inertia of a meter scale of mass 0.6 kg about an axis perpendicular to the scale and located at the 20 cm position on the scale in kg m square is (Breadth of the scale is negligible)

(a) 0.074 (b) 0.104 (c) 0.148 (d) 0.208 Ans. b (6)

Assertion : In case of bullet fired from gun, the ratio of kinetic energy of gun and bullet is equal to ratio of mass of bullet and gun. Reason : In firing, momentum is conserved.

(a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is …

2. In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown. The impulse at is

Ans. b (6)

A circular disc of radius R and thickness R/6 has moment of inertia I about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is

(a) I (b) 2I/8 (c) I/5 (d) I/10 Ans. c (5)

Assertion : If two protons are brought near one another, the potential energy of the system will increase. Reason : The charge on the proton is .+1.6×10-19C

A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x)= -kx+ax3 . Here k and a are positive constants. For x ≥ 0 , the functional from of the potential energy U(x) of the particle is

Answer:d (13)

A uniform cube of side a and mass m rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tilt about the edge is (assume that the cube does not slide)

(a) mg/4 (b) 2mg/3 (c) 3mg/4 (d) mg Ans. b (3)

38. Weights of 1g,2g,……..100g are suspended from the 1 cm, 2 cm, …… 100 cm, marks respectively of a light metre scale. Where should it be supported for the system to be in equilibrium

(a) 55 cm mark (b) 60 cm mark (c) 66 cm mark (d) 72 cm mark Ans. c (26)

Assertion : Mass and energy are not conserved separately, but are conserved as a single entity called mass-energy. Reason : Mass and energy conservation can be obtained by Einstein equation for energy.

37. A person supports a book between his finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of W then the person is producing a torque on the book of

(a) w. a/2 anticlockwise (b) w. b/2 anticlockwise (c) wa anticlockwise (d) wa clockwise Ans. b (72)

23. Assertion : Heavy water is used as moderator in nuclear reactor. Reason : Water cool down the fast neutron.

Assertion : Graph between potential energy of a spring versus the extension or compression of the spring is a straight line. Reason : Potential energy of a stretched or compressed spring, proportional to square of extension or compression.

36. When a force of 6.0 N is exerted at 30 degree to a wrench at a distance of 8 cm from the nut, it is just able to loosen the nut. What force F would be sufficient to loosen it, if it acts perpendicularly to the wrench at 16 cm from the nut

(a) 3 N (b) 6 N (c) 4 N (d) 1.5 N Ans. d (5)

Assertion : Wire through which current flows gets heated. Reason : When current is drawn from a cell, chemical energy is converted into heat energy.

A cubical block of side L rests on a rough horizontal surface with coefficient of friction μ . A horizontal force F is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is

(a) Infinitesimal (b) mg/4 (c) mg/2 (d) mg(1-μ) Ans. c (8)

20. Assertion : Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points. Reason : Gravitational forces are conservative forces.

Assertion : A quick collision between two bodies is more violent than slow collision, even when initial and final velocities are identical. Reason : The rate of change of momentum determine that force is small or large.

a) If both assertion and reason are true and the reason is the correct explanation of the assertion. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is …