A projectile of mass $M$ is fired so that the horizontal range is $4\, km$. At the highest point the projectile explodes in two parts of masses $M/4$ and $3M/4$ respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is .................. $\mathrm{km}$
$16$
$1$
$10$
$2$
A bomb of mass $3m$ kg explodes into two pieces of mass $m kg$ and $2m$ $kg$. If the velocity of m kg mass is $16 m/s$, the total kinetic energy released in the explosion is ................. $\mathrm{mJ}$
A balloon filled with helium rises against gravity increasing its potential energy. The speed of the balloon also increases as it rises. How do you reconcile this with the law of conservation of mechanical energy ? You can neglect viscous drag of air and assume that density of air is constant.
A bomb is projected upwards. At topmost point it explodes in three identical fragments. First fragment comes to ground in $10\ sec$. and others in $20\ sec$ each. Then the height reached by the original bomb is.........$m$
A particle of mass m moving with velocity ${V_0}$ strikes a simple pendulum of mass $m$ and sticks to it. The maximum height attained by the pendulum will be
A ball is projected from top of a tower with a velocity of $5\,\, m/s$ at an angle of $53^o$ to horizontal. Its speed when it is at a height of $0.45 \,\,m$ from the point of projection is ........ $m/s$