$A$ particle of mass $20\,g$ is released with an initial velocity $5\,m/s$ along the curve from the point $A,$ as shown in the figure. The point $A$ is at height $h = 10\,m$ from point $B.$ The particle slides along the frictionless surface. When the particle reaches point $B,$ its angular momentum about $O$ will be ......... $kg \cdot m^2/s$. [Take $g = 10\,m/s^2$]

Work equal to $25\,J$ is done on a mass of $2\,kg$ to set it in motion. If the whole of it is used to increase the kinetic energy,then the velocity acquired by the mass is ............ $m/s$.

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10 \ m$. If it dissipates $10 \%$ of its initial energy against air resistance,the speed with which the bob arrives at the lowest point is : [Use $g = 10 \ ms^{-2}$]

$A$ body of mass $2 \, kg$ is projected vertically upwards with a velocity of $2 \, m/s$. The kinetic energy $(K.E.)$ of the body just before striking the ground is ............. $J$.

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R).$
Assertion $(A):$ Kinetic energy of a system can increase without applying external force on the system.
Reason $(R):$ If external forces are absent,then the work done by internal forces is equal to the change in kinetic energy.
In the light of the above statements,choose the most appropriate answer from the options given below:

The total work done on a particle is equal to the change in its kinetic energy. This is applicable: