a bob hangs from a rigid support by an inextensible string of length $l$. If it is displaced through a distance $l$ ( from the lowest position) keeping the string straight & released,the speed of the bob at the lowest position is:

 

Two bodies of mass $m_1$ and $m_2$ $\left(m_2>m_1\right)$ are connected by a light inextensible string which passes through a smooth fixed pulley. The instantaneous power delivered by an external agent to pull $m_1$ with constant velocity $v$ is:

A small block slides with velocity  $0.5\sqrt{gr}$ on the horizontal frictionless surface as shown in the figure. The block leaves the surface at point $c$. The angle $\theta$ in the figure is:

Two identical block $A$ and $B$ are placed on two inclined planes as shown in diagram.Neglect air resistance and other friction. Choose the correct statement:

Statement $\mathrm{I}$: Kinetic energy of $\text{'}A\text{'}$ on sliding to $J$ will be greater then the kinetic energy $B$ on falling to $M$.

Statement $\mathrm{II}$: Acceleration of $\text{'}A\text{'}$ well be greater than acceleration 0f $\text{'}B\text{'}$ when both are released to slide on inclined plane.

Statement $\mathrm{III}$: Work done by external agent to move block slowly from position $B$ to $O$ is negative 

A particle $\text{'}A\text{'}$ of mass $\frac{10}{7}kg$ is moving in the positive x-direction. Its initial position is $x=0$ & initial velocity  is $1{\mathrm{ms}}^{-1}.$The velocity at $x=10\mathrm{m}$ is:(use the graph given)