$A$ 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

Two spheres $A$ and $B$ of masses $m_1$ and $m_2$ respectively collide. Sphere $A$ is at rest initially and sphere $B$ is moving with velocity $v$ along the $x$-axis. After the collision,sphere $B$ has a velocity of $\frac{v}{2}$ in a direction perpendicular to the original direction. The mass $A$ moves after the collision in the direction:

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A, B$ and $C$ are $m, 2m$ and $2m$ respectively. $A$ moves towards $B$ with a speed of $9 \ m/s$ and makes an elastic collision with it. Thereafter,$B$ makes a completely inelastic collision with $C$. All motions occur along the same straight line. The final speed of $C$ is $.... \ m/s$.

$A$ ball falls freely from a height of $180 \,m$ onto a hard horizontal floor and repeatedly bounces. If the coefficient of restitution is $0.5$, the average speed and average velocity of the ball before it ceases to rebound are respectively (acceleration due to gravity $= 10 \,ms^{-2}$)

Two identical blocks $A$ and $B$, each of mass $m$, resting on a smooth floor, are connected by a light spring of natural length $L$ and spring constant $k$. The spring is at its natural length. $A$ third identical block $C$ (mass $m$) moving with a speed $v$ along the line joining $A$ and $B$ collides with $A$. The maximum compression in the spring is proportional to

$A$ truck and a car are moving with equal velocity. On applying the brakes,both will stop after a certain distance. Which of the following is true?