A shell at rest on a smooth horizontal surface explodes into two fragments of masses $m_1$ and $m_2$. If just after explosion $m_1$ move with speed $u$, then work done by internal forces during explosion is
$\frac{1}{2}\left(m_1+m_2\right) \frac{m_2}{m_1} u^2$
$\frac{1}{2}\left(m_1+m_2\right) u^2$
$\frac{1}{2} m_1 u^2\left(1+\frac{m_1}{m_2}\right)$
$\frac{1}{2}\left(m_2-m_1\right) u^2$
A knife of mass $m$ is at a height $x$ from a large wooden block. The knife is allowed to fall freely, strikes the block and comes to rest after penetrating distance $y$. The work done by the wooden block to stop the knife is ..............
In a ballistics demonstration a police officer fires a bullet of mass $50.0 \;g$ with speed $200 \;m s ^{-1}$ on soft plywood of thickness $2.00 \;cm .$ The bullet emerges with only $10 \%$ of its initial kinetic energy. What is the emergent speed of the bullet?
$A$ small bucket of mass $M\, kg$ is attached to $a$ long inextensible cord of length $L\, m$ . The bucket is released from rest when the cord is in a horizontal position. At its lowest position, the bucket scoops up $m\, kg$ of water and swings up to a height $h$. The height $h$ in meters is
A sphere of mass $m$ comes down on a smooth inclined plane from a point $B$ at a height of $h$ from rest. The magnitude of change in momentum of the particle between the position $A$ and $C$ (assuming the angle of inclination of the plane as $\theta $ with respect to the horizontal) is
Under the action of a force, a $2 \,kg$ body moves such that its position $x$ as a function of time $t$ is given by $x=\frac{t^2}{3}$, where $x$ is in metres and $t$ in seconds. The workdone by the force in first two seconds is .......... $J$