The mass of the bob of a simple pendulum of length $L$ is $m$. If the bob is left from its horizontal position then the speed of the bob and the tension in the thread in the lowest position of the bob will be respectively

Two bodies of masses $m_1$ and $m_2$ are moving with same kinetic energy. If $P_1$ and $P_2$ are their respective momentum, the ratio $\frac{P_1}{P_2}$ is equal to

The work done by a force $\vec F = (-6x^3\hat i)\, N$, in displacing a particle from $x = 4\, m$ to $x = -2\, m$ is .............. $\mathrm{J}$

A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ $meter$ as shown in figure. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ............. $\mathrm{m}/ \mathrm{s}$

A long spring, when stretched by a distance $x,$ has the potential energy $u.$ On increasing the stretching to $nx.$ The potential energy of the spring will be

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 ............... $\mathrm{J}$