A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2 : 3. The smaller fragment moves with a velocity of 6 m/s. The kinetic energy of the larger fragment is

• 96 J

• 216 J

• 144 J

• 360 J

An electric bulb has a rated power of 50 W at 100 V. If it is used on an AC source 200 V, 50 Hz, a choke has to be used in series with it. This choke should have an inductance of

• 0.1 mH

• 1 mH

• 0.1 mH

• 1.1 H

Three concurrent co-planar forces 1 N, 2 N and 3 N acting along different directions on a body

• can keep the body in equilibrium if 2 N and 3 N act at right angle

• can keep the body in equilibrium if 1 N and 2 N act at right angle

• cannot keep the body in equilibrium

• can keep the body in equilibrium in 1 N and 3 N act at an acute angle

The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 m is

• 225 J

• 200 J

• 400 J

• 175 J

A certain vector in the xy-plane has an x-component of 4 m and a y-component of 10 m. It is then rotated in the xy-plane so that its x-component is doubled. Then, its new y-component is (approximately)

• 20 m

• 7.2 m

• 5.0 m

• 4.5 m

A police party is moving in a jeep at a constant speed v. They saw a thief at a distance x on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a. Which of the following relations is true if the police is able to catch the thief?

• v² < αx

• v² < 2αx

• v² ≥ 2αx

• v² = αx

A launching vehicle carrying an artificial satellite of mass m is set for launch on the surface of the earth of mass M and radius R. If the satellite is intended to move in a circular orbit of radius 7R, the minimum energy required to be spent by the launching vehicle on the satellite is (Gravitational constant= G)

• $\frac{\mathrm{GMm}}{\mathrm{R}}$

• $- \frac{13 \mathrm{G} \mathrm{M} \mathrm{m}}{14 \mathrm{R}}$

• $\frac{\mathrm{GMm}}{7\mathrm{R}}$

• $-\frac{\mathrm{G} \mathrm{M} \mathrm{m}}{14 \mathrm{R}}$

Two rectangular blocks A and B of masses 2 kg and 3 kg respectively are connected by a spring of constant 10.8 Nm^-1 and are placed on a frictionless horizontal surface. The block A was given an initial velocity of 0.15 ms^-1 in the direction shown in the figure. The maximum compression of the spring during the motion is

• 0.01 m

• 0.02 m

• 0.05 m

• 0.03 m

A body of mass m₁ = 4 kg moves at 5 i  m/s and another body of mass m₂ = 2 kg moves at 10 i  m/s. The kinetic energy of centre of mass is

• $\frac{200}{3}\mathrm{J}$

• $\frac{500}{3} \mathrm{J}$

• $\frac{400}{3}\mathrm{J}$

• $\frac{800}{3}\mathrm{J}$

A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of 8 rad-s^-2 produced in it due to the torque. Then, moment of inertia of the wheel is (g =10 ms^-2 )

• 2 kg-m²

• 1 kg-m²

• 4 kg-m²

• 8 kg-m²