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A ball is dropped on to a smooth horizontal plane from certain height h. Assuming the coefficient of restitution of impact is e.
The total distance covered by the ball till it stops
1. $\left(\frac{1-\mathrm{e}}{1+\mathrm{e}}\right)h$
2. $\left(\frac{1+{\mathrm{e}}^2}{1-{\mathrm{e}}^2}\right)h$
3. $\frac{{\mathrm{e}}^2\mathrm{h}}{1+{\mathrm{e}}^2}$
4. None of thesee

A ball is dropped on to a smooth horizontal plane from certain height h. Assuming the coefficient of restitution of impact is e.
Total time taken by ball till it stops bouncing
1. $\left(\frac{1-\mathrm{e}}{1+\mathrm{e}}\right)\sqrt{\frac{2h}{g}}$
2. $\left(\frac{1+\mathrm{e}}{1-\mathrm{e}}\right)\sqrt{\frac{2h}{g}}$
3. $e\sqrt{\frac{2h}{g}}$
4. None of these

A ball is dropped on to a smooth horizontal plane from certain height h. Assuming the coefficient of restitution of impact is e.
Total momentum delivered by the ball to the surface
1. ${\mathrm{mv}}_0\left(\frac{1+\mathrm{e}}{1-\mathrm{e}}\right)$
2. ${\mathrm{mv}}_0\sqrt{\frac{1-\mathrm{e}}{1+\mathrm{e}}}$
3. ${\mathrm{mv}}_0\left(\frac{1+\mathrm{e}}{1-\mathrm{e}}\right)$
4. None of these

A ball is thrown towards a floor with speed u. The coefficient of restitution between floor and ball is "e" . The speed with which ball rebounds is :

1. $\mathrm{v}=\mathrm{eu} \mathrm{sin\theta }$
2. $\mathrm{v}=\mathrm{eu} \mathrm{cos\theta }$
3. $\mathrm{v}=\mathrm{u}\sqrt{{\sin }^2\mathrm{\theta }+{\mathrm{e}}^2{\cos }^2\mathrm{\theta }}$
4. $\mathrm{v}=\mathrm{u}\sqrt{{\sin }^2\mathrm{\theta }-{\mathrm{e}}^2{\cos }^2\mathrm{\theta }}$

A pendulum consists of a wooden bob of mass m and length l. A bullet of ${\mathrm{m}}_1$ is fored towards the pendulum with a speed ${\mathrm{v}}_1$. The bullet emerges out of bob with a speed $\frac{{\mathrm{v}}_1}{3}$ and the bob just complete motion along a vertical circle, then ${\mathrm{v}}_1$ is :
1. $\left(\frac{\mathrm{m}}{{\mathrm{m}}_2}\right)\sqrt{5gl}$
2. $\frac{3}{2}\left(\frac{\mathrm{m}}{{\mathrm{m}}_1}\right)\sqrt{5gl}$
3. $\frac{2}{3}\left(\frac{{\mathrm{m}}_1}{\mathrm{m}}\right)\sqrt{5gl}$
4. $\frac{{\mathrm{m}}_1}{\mathrm{m}}{\left(gl\right)}^2$

The potential energy of a particle in a region of space is given as 
$U=\left(x^2+y^2+z^2+xy+yz+xz\right)$
The force acting on the particle at point (0,0,0)
1. 0 N
2. 3 N
3. 4 N
4. 7 N

A body is acted upon by a force which is inversely proportional to the distance covered. The work done will be proportional to 
1. s
2. ${\mathrm{s}}^2$
3. ${\mathrm{s}}^{1/2}$
4. None of these

A block of mass m slides down a rough inclined plane of inclination $\mathrm{\theta }$ with horizontal with zero initial velocity. The coefficient of friction between the block and plane is $\mathrm{\mu }$ with $\tan \theta >\mu$. Rate of work done by the force of friction at time t is 
1. ${\mathrm{\mu mg}}^2\mathrm{t} \mathrm{sin\theta }$
2. ${\mathrm{mg}}^2\mathrm{t}\left(\mathrm{sin\theta }-\mathrm{\mu cos\theta }\right)$
3. ${\mathrm{\mu mg}}^2\mathrm{t} \mathrm{cos\theta }\left(\mathrm{sin\theta }-\mathrm{\mu cos\theta }\right)$
4. ${\mathrm{\mu mg}}^2\mathrm{t} \mathrm{cos\theta }$

The velocity of a particle moving along a line varies with distance as $\mathrm{v}=\mathrm{a}\sqrt{\mathrm{x}}$ where a is a constant. The work done by all forces when the particle moves from x = 0 to x = l is ( mass of the particle is m)
1. 0
2. ${\mathrm{ma}}^2\mathrm{l}$
3. $\frac{1}{2}m{a}^{2}l$
4. $\frac{1}{3}m{a}^{2}l$

A particle is projected with speed u in air at an angle $\mathrm{\theta }$ with the horizontal. The graph showingg the variation of instantaneous power due to gravity P with time t will be 
1. 
2. 
3. 
4. 

The work done on a particle of mass m by a force, $\mathrm{K}\left[\frac{\mathrm{x}}{{\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)}^{3/2}}\hat{\mathrm{i}}+\frac{\mathrm{y}}{{\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)}^{3/2}}\hat{\mathrm{j}}\right]$ ( K being a constant of appropriate dimensions), when the particle is taken from the point (a,0) to the point (0,a) along a circular path of radius a about the origin in the x-y plane is
1. $\frac{2\mathrm{K\pi }}{\mathrm{a}}$
2. $\frac{\mathrm{K\pi }}{\mathrm{a}}$
3. $\frac{\mathrm{K\pi }}{2\mathrm{a}}$
4. 0

If ${\mathrm{W}}_1,{\mathrm{W}}_2 \mathrm{and} {\mathrm{W}}_3$ represent the work done in moving a particle from A to B along three different paths 1,2 and 3 respectively (as shown) in the gravitational field of a point mass m. Find the correct relation between ${\mathrm{W}}_1,{\mathrm{W}}_2 \mathrm{and} {\mathrm{W}}_3$

1. ${\mathrm{W}}_1>{\mathrm{W}}_2 > {\mathrm{W}}_3$
2. ${\mathrm{W}}_1={\mathrm{W}}_2 ={\mathrm{W}}_3$
3. ${\mathrm{W}}_1<{\mathrm{W}}_2 < {\mathrm{W}}_3$
4. ${\mathrm{W}}_2>{\mathrm{W}}_1 > {\mathrm{W}}_3$

If kinetic energy of a body is increased by 300 % then percentage change in momentum will be 
1. 100 % 
2. 150 %
3. 265 %
4. 73.2 %