$A$ body of mass $3 \text{ kg}$ is moving under the action of a force which causes a displacement of $\left(\frac{t^3}{3}\right) \text{ m}$, where '$t$' is time in seconds. The work done by the force in the first $2 \text{ seconds}$ is: (in $\text{ J}$)

$A$ small sphere of mass $m$ and radius $r$ slides down the smooth surface of a large hemispherical bowl of radius $R$. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point $A$ of the bowl will be [given, moment of inertia of sphere $= \frac{2}{5} mr^2$].

$A$ block weighing $20 \ N$ travels down a smooth curved track $AB$ joined to a rough horizontal surface (figure). The rough surface has a friction coefficient of $0.40$ with the block. If the block starts slipping on the track from a point $1.0 \ m$ above the horizontal surface,the distance it will move on the rough surface is: (in $m$)

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

$A$ 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,initially at rest on a frictionless horizontal surface,is acted upon by a horizontal force which is constant in size and direction. $A$ graph is plotted between the work done $(W)$ on the particle and the speed of the particle $(v)$. If there are no other horizontal forces acting on the particle,the graph would look like: