Physics : Work, Energy and Power

A particle is displaced from a position $\left(2\hat{\mathrm{i}} - \hat{\mathrm{j}} + \hat{\mathrm{k}}\right)$ to another position $\left(3\hat{\mathrm{i}} + 2\hat{\mathrm{j}} - 2\hat{\mathrm{k}}\right)$ under the action of the force of $\left(2\hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}}\right)$. The work done by the force in an arbitrary unit is

• 8

• 10

• 12

• 16

In elastic collision

• both momentum and kinetic energies are conserved

• both momentum and kinetic energies are not conserved

• only energy is conserved

• only mechanical energy is conserved

A ball is released from the top of a tower. The ratio of work done by force of gravity in first, second and third second of the motion of the ball is

• 1 : 2 : 3

• 1 : 4 : 9

• 1 : 3 : 5

• 1 : 5 : 3

When the kinetic energy of a body is doubled, its momentum increases by times

• $\sqrt{2}$

• 2

• 4

• $2\sqrt{2}$

A body rolls down an inclined plane. If its kinetic energy of rotation is 40% of its kinetic energy of translation, then the body is

• solid cylinder

• solid sphere

• disc

• ring

A 10 kg object collides with stationary 5 kg object and after collision they stick together and move forward with velocity 4 ms^-1. What is the velocity with which the 10 kg object hit the second one ?

• 4 ms^-1

• 6 ms^-1

• 10 ms^-1

• 12 ms^-1

When a force is applied on a moving body, its motion is retarded. Then the work done is

• positive

• negative

• zero

• positive and negative

An α-particle of mass m suffers one dimensional elastic collision with a nucleus of unknown mass. After the collision the α-particle is scattered directly backwards losing 75% of its kinetic energy. Then the mass of the nucleus is

• m

• 2m

• 3m

• $\frac{3}{2} \mathrm{m}$

An elastic ball is dropped from a height h and it rebounds many times from the floor. If the coefficient of restitution is e, the time interval between the second and the third impact, is

• ev/g

• e²v/g

• ${\mathrm{e}}^2\sqrt{\left(\frac{8\mathrm{h}}{\mathrm{g}}\right)}$

• ${\mathrm{e}}^2 \sqrt{\left(\frac{\mathrm{h}}{\mathrm{g}}\right)}$

An object of mass m is attached to light string which passess through a hollow tube. The object is set into rotation in a horizontal circle of radius, r₁. If the string is pulled shortening the radius to r₂, the ratio of new kinetic energy to the original kinetic energy is

• ${\left(\frac{{\mathrm{r}}_2}{{\mathrm{r}}_1}\right)}^2$

• ${\left(\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}\right)}^2$

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

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