Two bodies of masses $m_{1}$ and $m_{2}$ are acted upon by a constant force $F$ for a time $t$. They start from rest and acquire kinetic energies,$E_{1}$ and $E_{2}$ respectively. Then $\frac{E_{1}}{E_{2}}$ is

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:

The rate of doing work by a force acting on a particle moving along the $x$-axis depends on the position $x$ of the particle and is equal to $2x$. The velocity of the particle is given by the expression:

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

$A$ $2\,kg$ 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 $110\,N$ and the spring constant is $1000\,N/m$. The spring compresses by ........ $cm$.

In a one-dimensional collision between two particles,their relative velocity is $\vec{v}_1$ before the collision and $\vec{v}_2$ after the collision.