Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by
$\frac{1}{2}\,m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
$m\,\frac{v}{{{t_1}}}{\kern 1pt} {t^2}$
$\frac{1}{2}\,{\left( {\frac{{mv}}{{{t_1}}}} \right)^2}{\kern 1pt} {t^2}$
$\frac{1}{2}\,m\,\frac{v^2}{{{t^2_1}}}{\kern 1pt} {t^2}$
A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be
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 mass $m$ moving horizontally with velocity $v_0$ strikes a pendulum of mass $m$. If the two masses stick together after the collision, then the maximum height reached by the pendulum is
A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is
Work done by the frictional force is