A particle suspended by a light inextensible thread of length l is projected horizontally from its lowest position with velocity $\sqrt{4gl}$. The height from its lowest position at which particle will leave the circular path is:

1.  $\frac{3\mathrm{l}}{2}$

2.  $\frac{5l}{3}$

3.  $\frac{4l}{3}$

4.  2l

A mass M is suspended by a spring having a spring constant K. In equilibrium position mass M is given a speed u. Find further extension in the spring.

1.  $\sqrt{\frac{\mathrm{M}}{\mathrm{K}}}\mathrm{u}$

2.  $\sqrt{\frac{2\mathrm{M}}{\mathrm{K}}}\mathrm{u}$

3.  $\sqrt{\frac{\mathrm{M}}{\mathrm{K}}}\mathrm{u} + \frac{\mathrm{Mg}}{\mathrm{K}}$

3.  $\sqrt{\frac{2\mathrm{M}}{\mathrm{K}}}\mathrm{u} + \frac{\mathrm{Mg}}{\mathrm{K}}$

A ball 'P strikes elastically with another identical ball Q resting on a smooth surface with velocity v. The ratio of the speeds of ${\mathrm{v}}_{\mathrm{P}} : {\mathrm{v}}_{\mathrm{e}}$ two balls after the collision is

(1)  1: $\sqrt{3}$

(2)  $\sqrt{3}$:1

(3)  1:2

(4)  $\sqrt{3}$:2

A block of mass 20 kg is being brought down by a chain. If block acquires a speed of 2 m/s in dropping down 2 m. Find work done by the chain during the process. (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

(1)  -360 J

(2)  400 J

(3)  360 J

(4)  -280 J

A ball is dropped from a height h on a stationary floor and rebounds. If the coefficient of restitution is 0.5, then the total distance covered by the ball before it strikes the floor for 3rd time is:

1.  2h

2.  $\frac{13\mathrm{h}}{8}$

3.  $\frac{3\mathrm{h}}{2}$

4.  $\frac{4\mathrm{h}}{3}$

A particle is projected at a time \(t=0\) with a speed \(v_{0}\)${\mathrm{}}_{}$ and at an angle with the horizontal in a uniform gravitational field. Then which of the following graph represents power delivered by gravitational force against time \((t)\)?

1.		2.
3.		4.

Two balls having different masses are moving towards each other with speed 30 m/s and 20 m/s as shown in figure (i). Their velocities after collision become 20 m/s and 30 m/s as shown in the figure (ii), then the coefficient of restitution is:

(1)  1

(2)  0.5

(3)  0.4

(4)  0.2

Which of the following is not correct?

(1)  Force of friction is non-conservative.

(2)  If R is the horizontal range of an oblique the projectile, then the kinetic energy of the projectile is minimum after covering a horizontal the distance of R/2 considering air resistance.

(3)  Viscous force is a non-conservative force.

(4)  Work done in stretching a spring successively by length x from natural length are in the ratio 1:3.

One sphere collides with another sphere of double its mass. While heavier mass was at rest initially. The ratio of their respective speeds after the collision will be (Coefficient of restitution = e)

1.  $\frac{1 - 2\mathrm{e}}{1 - \mathrm{e}}$

2.  $\frac{1 - 2\mathrm{e}}{1 + \mathrm{e}}$

3.  $\frac{1 - \mathrm{e}}{1 + 2\mathrm{e}}$

4.  $\frac{1 + 2\mathrm{e}}{1 - \mathrm{e}}$

A particle of mass ${\mathrm{m}}_1$ makes an elastic, one-dimensional collision with another stationary particle of mass ${\mathrm{m}}_2$. The fraction of kinetic energy of ${\mathrm{m}}_1$ carried away by ${\mathrm{m}}_2$ is

1.  $\frac{{\mathrm{m}}_1^2}{{\mathrm{m}}_2^2}$

2.  ${\left(\frac{{\mathrm{m}}_1^2}{{\mathrm{m}}_2^2}\right)}^{-1}$

3.  $\frac{{\mathrm{m}}_1 - {\mathrm{m}}_2}{{\left({\mathrm{m}}_1 + {\mathrm{m}}_2\right)}^2}$

4.  $\frac{4{\mathrm{m}}_1{\mathrm{m}}_2}{{\left({\mathrm{m}}_1 + {\mathrm{m}}_2\right)}^2}$