$A$ particle of mass $2 \,kg$ travels along a straight line with velocity $v = a \sqrt{x}$,where $a$ is a constant. The work done by the net force during the displacement of the particle from $x = 0$ to $x = 4 \,m$ is .........

$A$ particle of mass $m$ slides down along a frictionless inclined plane $AC$ as shown in the figure. The kinetic energy of the particle at point $C$ is:

$A$ lorry and a car moving with the same kinetic energy $(K.E.)$ are brought to rest by applying the same retarding force. Then:

$A$ pendulum bob on a $2\, m$ string is displaced $60^\circ$ from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path? (Take $g = 9.8\, m/s^2$)

$A$ body dropped from height $H$ reaches the ground with a speed of $1.1 \sqrt{gH}$. Calculate the work done by air friction in terms of $mgH$.

$A$ block of mass $\sqrt{2} \, kg$ is released from the top of an inclined smooth surface as shown in the figure. If the spring constant of the spring is $100 \, N/m$ and the block comes to rest after compressing the spring by $1 \, m$,then the total distance travelled by the block along the incline before it comes to rest is ......... $m$.