Three balls, $A, B$ and $C$ are released and all reach the point $X$ (shown in the figure). Balls $A$ and $B$ are released from two identical structures, one kept on the ground and the other at height $h$, from the ground as shown in the figure. They take time $t_A$ and $t_B$ respectively to reach $X$ (time starts after they leave the end of the horizontal portion of the structure). The ball $C$ is released from a point at height $h$, vertically above $X$ and reaches $X$ in time $t_C$. Choose the correct option.
$t_C < t_A < t_C$
$t_C=t_A=t_C$
$t_C=t_A < t_C$
$t_B < t_A=t_C$
A ball is allowed to fall from a height of $10 \,m$. If there is $40 \%$ loss of energy due to impact, then after one impact ball will go up by ........ $m$
A projectile is fired at a speed of $100\, m/sec$ at an angle of $37^o$ above the horizontal. At the highest point, the projectile breaks into two parts of mass ratio $1:3$ , the smaller coming to rest. Then the distance of heavier part from the launching point is ............... $\mathrm{m}$
A projectile is moving at $20\,m/sec$ at its highest point where it breaks into two equal parts due to an internal explosion. One part moves vertically up at $30\,m/sec$ . Then the other part will move at ............. $\mathrm{m}/ \mathrm{s}$
An ice block is melting at a constant rate $\left| {\,\frac{{dm}}{{dt}}\,} \right|= \mu$ . Its initial mass is $m_0$ and it is moving with velocity on a frictionless horizontal surface. The distance travelled by it till it melts completely is :
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 .................. $\mathrm{km}$