Morning breakfast provides $5000 \,cal$ of energy to a $60 \,kg$ person. The efficiency of the person is $30 \%$. The height up to which the person can climb using the energy obtained from the breakfast is ......... $m$.

$A$ $2 \ kg$ block slides on a horizontal floor with a speed of $4 \ m/s$. It strikes an uncompressed spring and compresses it until the block is motionless. The kinetic friction force is $15 \ N$ and the spring constant is $10,000 \ N/m$. The spring compresses by ............. $cm$.

$A$ ball is held in the position shown with a string of length $L = 1 \, m$ just taut and then projected horizontally with a velocity of $u = 3 \, m/s$. If the string becomes taut again when it is vertical,the angle $\theta$ is given by ........ $^o$.

In a one-dimensional collision between two identical particles $A$ and $B$, $B$ is stationary and $A$ has momentum $p$ before impact. During impact, $B$ gives impulse $J$ to $A$.

Two solid rubber balls $A$ and $B$ have masses $200 \ g$ and $400 \ g$ respectively. They are moving towards each other,with ball $A$ having a velocity of $0.3 \ m/s$. After the collision,both balls come to rest. What is the velocity of ball $B$ in $m/s$?

An object of mass $M$ is at rest on a smooth horizontal surface. Objects of different masses collide head-on elastically with the object of mass $M$. All colliding objects have the same fixed kinetic energy $E$,and in each case,mass $M$ is initially at rest. The kinetic energy transferred to the stationary mass $M$ depends on the linear momentum $P$ of the incoming colliding mass. How does the energy transferred to $M$ vary with the linear momentum $P$?