$A$ free body of mass $8 \, kg$ is travelling at $2 \, m/s$ in a straight line. At a certain instant,the body splits into two equal parts due to an internal explosion which releases $16 \, J$ of energy. Neither part leaves the original line of motion. Finally:

  • A
    Both parts continue to move in the same direction as that of the original body.
  • B
    One part comes to rest and the other moves in the same direction as that of the original body.
  • C
    One part comes to rest and the other moves in the direction opposite to that of the original body.
  • D
    One part moves in the same direction and the other in the direction opposite to that of the original body.

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$A$ man throws a ball to a height of $12 \ m$,where it reaches with a speed of $12 \ m/s$. If the man throws the ball such that it just reaches this height,what percentage of energy would he have saved?

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Fill in the blanks:
$(a)$ In electricity consumption,$1$ unit is equal to .......... Joules of work.
$(b)$ $A$ body falling from a height of $10 \ m$ onto hard ground loses $20 \%$ of its energy. It can reach a height of .............
$(c)$ $A$ particle moves in a circular path of radius $a$ under the influence of an attractive force with potential energy $U = -\frac{k}{2r^2}$. Its total energy is = .......
$(d)$ Converting a mass of $1 \ \mu g$ into energy yields ........ energy.

$A$ shell is fired from a cannon with velocity $v \text{ m/s}$ at an angle $\theta$ with the horizontal direction. At the highest point in its path,it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon. The speed in $\text{m/s}$ of the other piece immediately after the explosion is:

Two bodies $A$ and $B$ of masses $1.5 \ kg$ and $3 \ kg$ are moving with velocities $20 \ m \ s^{-1}$ and $15 \ m \ s^{-1}$ respectively. If the same retarding force is applied on the two bodies,then the ratio of the distances travelled by the bodies $A$ and $B$ before they come to rest is

Starting from rest on her swing at initial height $h_0$ above the ground,Saina swings forward. At the lowest point of her motion,she grabs her bag that lies on the ground. Saina continues swinging forward to reach maximum height $h_1$. She then swings backward and when reaching the lowest point of motion again,she simply lets go of the bag,which falls freely. Saina's backward swing then reaches maximum height $h_2$. Neglecting air resistance,how are the three heights related?

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