A sphere of mass $m$ travelling at constant speed $v$ strike another sphere of same mass. If coefficient of restitution is $e$, then ratio of velocity of both spheres just after collision is :-
$\frac{1-e}{1+e}$
$\frac{1+e}{1-e}$
$\frac{e+1}{e-1}$
$\frac{e-1}{e+1}$
Consider two carts, of masses $m$ and $2m$ , at rest on an air track. If you push both the carts for $3\,s$ exerting equal force on each, the kinetic energy of the light cart is
Underline the correct alternative :
$(a)$ When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered.
$(b)$ Work done by a body against friction always results in a loss of its kinetic/potential energy.
$(c)$ The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system.
$(d)$ In an inelastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy/total linear momentum/total energy of the system of two bodies.
A body of mass ${m_1}$ moving with uniform velocity of $40 \,m/s$ collides with another mass ${m_2}$ at rest and then the two together begin to move with uniform velocity of $30\, m/s$. The ratio of their masses $\frac{{{m_1}}}{{{m_2}}}$ is
A bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the bullet will be
$A$ ball is projected from ground with a velocity $V$ at an angle $\theta$ to the vertical. On its path it makes an elastic collison with $a$ vertical wall and returns to ground. The total time of flight of the ball is