A ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is $7 \mathrm{~ms}^{-1}$ and the coefficient of restitution is 0.75 , the total distance travelled by the ball before it comes to rest is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A solid cylinder rolls down an inclined plane without slipping. If the translation kinetic energy of the cylinder is 140 J . The total kinetic energy of the cylinder is

Two blocks of masses $m$ and $2 m$ are connected by a massless string which passes over a fixed frictionless pulley. If the system of blocks is released from rest, the speed of the centre of mass of the system of two blocks after a time of 5.4 s is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The displacement of a particle executing simple harmonic motion is $y=A \sin (2 t+\phi) \mathrm{m}$, where $t$ is time in second and $\phi$ is phase angle. At time $t=0$, the displacement and velocity of the particle are 2 m and $4 \mathrm{~ms}^{-1}$. The phase angle, $\phi=$