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 bomb of mass $12\,\,kg$  at rest explodes into two fragments of masses in the ratio $1 : 3.$  The $K.E.$  of the smaller fragment is $216\,\,J.$  The momentulm of heavier fragment is (in $kg-m/sec$ )

A particle of mass $m$ moving horizontally with $v_0$ strikes $a$ smooth wedge of mass $M$, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to $a$ height $h$. Choose the correct statement(s) related to particle $m$ 

State and establish principle of conservation of mechanical energy.

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 .................. $\mathrm{km}$

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 ........ $m$