Question 1 :
A completely inelastic collision is one in which the two colliding particles-

Question 2 :
Assertion: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Reason: Principle of conservation of momentum holds true for all kinds of collisions.

Question 3 :
A body of mass $ m_1 $ moving with a velocity 10 m/s collides elastically with another body at rest of mass $ m_2 $. After collision the velocites of the two bodies are 2 m/s and 5 m/s respectively along the direction of motion of $ m_1 $. The ration of $ \dfrac { m_ {1} }{ m_ {2} }  is $

Question 4 :
The gravitational potential energy of a body is ________ to its height above the surface of the Earth.

Question 6 :
Two balls $A$ and $B$ having masses $m\ \text{kg}$ and $2 m\ \text{kg,}$ moving with speeds $21\ \text{m/s}$ and $4\ \text{m/s}$ respectively in opposite direction, collide head on. After collision $A$ moves with a speed of $1\ \text{m/s}$ in the same direction, then incorrect statement is :

Question 8 :
A ball is dropped from a height of $20$m on a floor for which $e=1/2$. The height attained by the ball after the second collision.

Question 9 :
A ball of mass $m$ is thrown vertically up with an initial velocity so as to reach a height $h$. The correct statement is:

Question 11 :
A particle of mass $m$ moving with a velocity $\left( 3\hat { i } +2\hat { j }  \right) m{s}^{-1}$ collides with a stationary body of mass $M$ and finally moves with a velocity $\left( -2\hat { i } +\hat { j }  \right) m{s}^{-1}$.  If $\cfrac{M}{m}=\cfrac{1}{13}$, then:

Question 12 :
A body moving at $2$ m/s can be stopped over a distance $x$. lf its kinetic energy is doubled, how long will it go before coming to rest, retarding force remains unchanged?

Question 13 :
Which one of the following statements does hold good when two balls of masses ${m}_{1}$ and ${m}_{2}$ undergo elastic collision?

Question 14 :
The amount of work done is pumping water out of a cubical vessel of height 1 m is nearly (Given $\rho_{water}=1000\ kg/m^3$)

Question 15 :
If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest

Question 16 :
A body dropped freely from a height h on to a horizontal plane, bounces up and down and finally comes to rest.The coefficient of restitution is e. The ratio of velocities at the beginning and after two rebounds is

Question 17 :
A body of mass 10 gm moving with a velocity of $20 cms^{-1}$ collides with a stationary mass of 90 gm. The collision is perfectly inelastic. Find the percentage loss of kinetic energy of the system.

Question 18 :
In an elastic collision of two particles the following is conserved

Question 19 :
A smooth small spherical ball of mass m, moving with velocity u collides head on with<br>another small spherical ball of mass 3 m, which was intially at rest. Two-third of the initial kinetic energy of the system is lost. The coefficient of restitution between the spheres is<br>

Question 20 :
When a force retards the motion of a body, the work done is :<br/>

Question 21 :
Three forces $ \overrightarrow P $ , $ \overrightarrow Q $ and $ \overrightarrow R $ are acting at a point in a plane. The angle between $ \overrightarrow P $ and $\overrightarrow Q $ , $ \overrightarrow Q $ and $ \overrightarrow R $ are $ 150^{\circ} $ and $ 120^{\circ} $ respectively. Then for the equilibrium, forces $ \overrightarrow P $ , $ \overrightarrow Q $ and $ \overrightarrow R $ are in the ratio :-

Question 22 :
A sphere of mass $m$ is moving with a velocity $ ( 4 \hat{i} - \hat{j} ) m/s$ hits a frictionless and rebounds with a velocity $ ( \hat{i} + 3 \hat{j} ) m/s $ . The coefficient of restitution between the sphere and the surface is :

Question 23 :
Calculate the work done by a coolie in carrying a load of mass $10$ kg on his head when he walks uniformly a distance of $5$ in the (i) horizontal direction&#160; (ii) vertical direction. ( Take $g= 10 m/s^2$).

Question 24 :
A block of mass $m$ is attached to one end of a massless spring of spring constant $k$. The other end of spring is fixed to a wall. The block can move on a horizontal rough surface. The coefficient of friction between the block and the surface is $\mu$. Then the compression of the spring for which maximum extension of the spring becomes half of maximum compression is:

Question 25 :
A small body of mass m is located on a horizontal plane at the point O. The body acquires a horizontal velocity $\displaystyle v_{0}$ due to friction. Find, the mean power developed by the friction force during the motion of the body, if the frictional coefficient $\displaystyle \mu = 0.27, m= 1.0kg\:and\:v_{0}= 1.5m/s.$