Work, Energy and Power

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 ms^-1. The kinetic energy of the larger fragment is

• 96 J

• 216 J

• 144 J

• 360 J

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

If the linear momentum of a body is increased by 50%, then the kinetic energy of that body increases by

• 100 %

• 125 %

• 225 %

• 25 %

A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity = 9.8 ms^-2)

• 5 m

• 2.5 m

• 10 m

• 12.5 m

A solid sphere of mass m rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is v. The kinetic energy of the sphere at the bottom is

• $\frac{1}{2} {\mathrm{mv}}^2$

• $\frac{5}{3} {\mathrm{mv}}^2$

• $\frac{2}{5} {\mathrm{mv}}^2$

• $\frac{7}{10} {\mathrm{mv}}^2$

A body of mass m is travelling with a velocity u. When a constant retarding force F is applied, it comes to rest after travelling a distances s₁. If the initial velocity is 2u, with the same force F, the distance travelled before it comes to rest is s₂. Then,

• s₂ = 4s₁

• s₂ = 2s₁

• ${\mathrm{s}}_2 = \frac{{\mathrm{s}}_1}{2}$

• s₂ = s₁

Two bodies ofmasses m₁ and m₂ are acted upon by a constant force F for a time t. They start from rest and acquire kinetic energies, E₁ and E₂ respectively. Then $\frac{{\mathrm{E}}_1}{{\mathrm{E}}_2}$ is

• $\frac{\sqrt{{\mathrm{m}}_1{\mathrm{m}}_2}}{{\mathrm{m}}_{1 }+ {\mathrm{m}}_2}$

• $\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}$

• $\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}$

• 1

Two fixed charges A and B of 5 µC each are separated by a distance of 6 m. C is the mid point of the line joining A and B. A charge Q of −5μC is shot perpendicular to the line joining A and B through C with a kinetic energy of 0.06 J. The charge Q comes to rest at a point D. The distance CD is

• 4 m

• 3 m

• $\sqrt{3} \mathrm{m}$

• $3\sqrt{3} \mathrm{m}$

A gun fires a small bullet with kinetic energy K. Then kinetic energy of the gun while recoiling is

• K

• more than K

• less than K

• $\sqrt{\mathrm{K}}$

A truck accelerates from speed v to 2v. Work done in during this is

• three times as the work done in accelerating it from rest to v

• same as the work done in accelerating it from rest to v

• four times as the work done in accelerating it from rest to v

• ess than the work done in accelerating it from rest to v