The potential energy of a particle oscillating along $x-$ axis  is given as $U = 20 + (x - 2)^2$  where $U$  is in joules and $x$ in $meters$ . Total mechanical energy of the particle is $36\,\, J$ . Maximum kinetic energy of the particle is ................ $\mathrm{J}$

A wedge of mass $M = 4\,m$ lies on a frictionless plane. A particle of mass $m$ approaches the wedge with speed $v$. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by

A body of mass $10\, kg$ is released from a tower of height $20\,m$ and body acquires a velocity of $10\,ms^{-1}$ after falling through the distance $20\,m$ . The work done by the push of the air on the body is:- ................. $\mathrm{J}$  (Take $g = 10\, m/s^2$ )

A shell at rest on a smooth horizontal surface explodes into two fragments of masses $m_1$ and $m_2$. If just after explosion $m_1$ move with speed $u$, then work done by internal forces during explosion is

A mass of $M\ kg$ is suspended by a weightless string. The horizontal force that is displace it until the string makes an angle of $45^o $ with the initial vertical direction is

A block of mass $0.18 \ kg$ is attached to a spring of force-constant $2 \ N / m$. The coefficient of friction between the block and the floor is $0.1$ . Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of $0.06 \ m$ and comes to rest for the first time. The initial velocity of the block in $m / s$ is $V = N / 10$. Then $N$ is