A body of mass $5 \,kg$  explodes at rest into three fragments with masses in the ratio $1 : 1 : 3$. The fragments with equal masses fly in mutually perpendicular directions with speeds of $21 \,m/s$. The velocity of the heaviest fragment will be

A shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/3$ remains stationary. The velocity of other part will be

$A$ parallel beam of particles of mass $m$ moving with velocity $v$ impinges on $a$ wall at an angle $\theta$ to its normal . The number of particles per unit volume in the beam is $n$ . If the collision of particles with the wall is elastic, then the pressure exerted by this beam on the wall is :

Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any change in speed, as shown in Figure. What is

$(i)$ the direction of the force on the wall due to each ball?

$(ii)$ the ratio of the magnitudes of impulses imparted to the balls by the wall ?

A man is standing on a balance and his weight is measured. If he takes a step in the left side, then weight

A cannon ball is fired with a velocity $200\, m/sec$ at an angle of $60° $ with the horizontal. At the highest point of its flight it explodes into $3$ equal fragments, one going vertically upwards with a velocity $100 \,m/sec$, the second one falling vertically downwards with a velocity $100\, m/sec$. The third fragment will be moving with a velocity