$A$ machine which is $70 \%$ efficient raises a $10 \,kg$ body through a certain distance and spends $100 \,J$ energy. The body is then released. On reaching the ground, the kinetic energy of the body will be

$A$ 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?

$A$ block $C$ of mass $m$ is moving with velocity $v_0$ and collides elastically with block $A$ of mass $m$ which is connected to another block $B$ of mass $2m$ through a spring of spring constant $k$. What is $k$ if $x_0$ is the compression of the spring when the velocity of $A$ and $B$ is the same?

$A$ rubber ball is dropped from a height of $5 \ m$ on a planet,where the acceleration due to gravity is not known. On bouncing,it rises to $1.8 \ m$. The ball loses its velocity on bouncing by a factor of

In a perfectly inelastic collision, two spheres made of the same material with masses $15 \ kg$ and $25 \ kg$, moving in opposite directions with speeds of $10 \ m/s$ and $30 \ m/s$, respectively, strike each other and stick together. The rise in temperature (in $^{\circ}C$), if all the heat produced during the collision is retained by these spheres, is: (specific heat of sphere material $31 \ cal/kg \cdot ^{\circ}C$ and $1 \ cal = 4.2 \ J$)

Three particles $A, B$,and $C$ of equal mass move with speed $V$ as shown to strike at the centroid of an equilateral triangle. After the collision,$A$ comes to rest and $B$ retraces its path with speed $V$. The speed of $C$ after the collision is: