A particle of mass 10 kg is moving with a velocity of $10\sqrt{x}$ m/s, where x is displacement. The work done by net force during the displacement of the particle from x = 4 m to x = 9 m is:

(1)  1250 J

(2)  1000

(3)  3500 J

(4)  2500 J

Two bodies A and B of mass m and 2m respectively are placed on a smooth floor as shown. They are connected by a spring of constant k. If a third body C of mass m moves with a velocity ${\mathrm{v}}_0$ along the line joining A and B and collides head-on elastically with A, then speed of A at the instant of maximum compression is

1.  ${\mathrm{v}}_0$

2.  $\frac{{\mathrm{v}}_0}{2}$

3.  $\frac{{\mathrm{v}}_0}{4}$

4.  $\frac{{\mathrm{v}}_0}{3}$

A block of mass m is allowed to slide down a fixed smooth inclined plane of inclination $\mathrm{\theta }$and slope length L. What is the power developed by the force of gravity, when the block reaches the bottom?

1.  $\sqrt{2{\mathrm{m}}^2\mathrm{L}{\left(\mathrm{gsin\theta }\right)}^3}$

2.  $\frac{2}{3}{\mathrm{Lg}}^2\sin \mathrm{\theta }$

3.  $\sqrt{\frac{2}{3}{\mathrm{m}}^2{\mathrm{Lg}}^3}$

4.  $\mathrm{mg}\sqrt{2\mathrm{gL} \sin \mathrm{\theta }}$

Which of the following statement is correct regarding potential energy?

(1)  Change in potential energy depends upon reference point.

(2)  Potential energy does not depend upon reference point.

(3)  Potential energy can be defined for any field.

(4)  Change in potential energy of any particle is equal to work done by external force for moving the particle in equilibrium in a conservative field.

A body A of mass 10 kg at rest starts slipping from the top of the inclined plane of height 10 m as shown. If it reaches the ground at 10 m/s, then work done by friction is

(1)  500 J

(2)  -500 J

(3)  1000 J

(4)  -1000 J

A body is released from the top of an inclined smooth plane of inclination $\mathrm{\theta }$. It reaches the bottom with speed u. If the angle of inclination is doubled keeping the height unchanged, then the speed of the object on reaching on the ground is

(1)  u

(2)  2u

(3)  $\mathrm{u}\sqrt{2\cos \mathrm{\theta }}$

(4)  $\frac{\mathrm{u}}{\sqrt{2\sin \mathrm{\theta }}}$

Select the correct statement. Work is done by the internal forces on the system

(1)  maybe zero.

(2)  must be greater than zero.

(3)  must be less than zero.

(4)  must be zero.

The potential energy of a particle of mass 1 kg free to move along the X-axis is given by \(U(x) = (3x^2-4x+6)~\text{J}\). The force acting on the particle at x = 0 will be:

1.  2$\hat{\mathrm{i}}$ N

2.  -4$\hat{\mathrm{i}}$ N

3.  5$\hat{\mathrm{i}}$ N

4.  4$\hat{\mathrm{i}}$ N

A block of mass m is attached with a spring of spring constant k as shown in the figure. Another block of mass 2m moving with speed v hits the spring. Speed of blocks at the instant of maximum compression of spring is:

1.  $\frac{\mathrm{v}}{3}$

2.  $\frac{\mathrm{v}}{2}$

3.  $\frac{2\mathrm{v}}{3}$

4.  $\frac{3\mathrm{v}}{2}$

The potential energy of a particle of mass m varies as $U=a{x}^2+by.$ The magnitude of the acceleration of the particle at (0, 3) is (symbols have their usual meaning)

1.  $\sqrt{\frac{\mathrm{b}}{\mathrm{m}}}$

2.  $\sqrt{\frac{3\mathrm{b}}{\mathrm{m}}}$

3.  $\frac{\mathrm{b}}{\mathrm{m}}$

4.  Zero