A mass of $0.5\, kg$ moving with a speed of $1.5\, m/s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k=50\,N/m$. The maximum compression of the spring would be ................. $\mathrm{m}$

A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are

A mass $m$ moving horizontally with velocity $v_0$ strikes a pendulum of mass $m$. If the two masses stick together after the collision, then the maximum height reached by the pendulum is

A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ is .............

A particle is made to move from the origin in three spells of equal distances, first along the $x-$ axis, second parallel to $y-$ axis and third parallel to $z-$ axis. One of the forces acting on it is has constant magnitude of $50\,N$ and always acts along the direction of motion. Work done by this force in the three spells of motion are equal and total work done in all the three spells is $300\,J$. The final coordinates of the particle will be

A ball is dropped from height $h$ on a plane. If the coefficient of restitution of the plane is $e$ and if ball hits ground two times, the height upto which it reaches after two jumps, will be