$A$ body of mass $5 \ kg$ is placed on a horizontal surface with a coefficient of friction $\mu = 0.2$. It is pulled by a horizontal force of $25 \ N$ for a distance of $10 \ m$. The kinetic energy gained by the body is ..... $J$. (Take $g = 10 \ m/s^2$)

$A$ ball is moving to and fro about the lowest point $A$ of a smooth hemispherical bowl. If it is able to rise up to a height of $20 \,cm$ on either side of $A$,its speed at $A$ must be .......... $m/s$ (Take $g = 10 \,m/s^2$,mass of the body = $5 \,g$).

$A$ particle of mass $m$ moves with a velocity $v = a\sqrt{x}$,where $a$ is a constant and $x$ is the displacement. Find the total work done by all forces during the displacement from $x = 0$ to $x = d$.

The potential energy of a $1 \ kg$ particle free to move along the $x-$axis is given by: $U(x) = (\frac{x^4}{4} - \frac{x^2}{2}) \ J$. The total mechanical energy of the particle is $2 \ J$. Then,the maximum speed (in $m/s$) is:

$A$ block of mass $m$ is sliding down an inclined plane with constant speed. At a certain instant $t_0$,its height above the ground is $h$. The coefficient of kinetic friction between the block and the plane is $\mu$. If the block reaches the ground at a later instant $t_g$,then the energy dissipated by friction in the time interval $(t_g - t_0)$ is

$A$ spherical ball of mass $2 \text{ kg}$ falls from a height of $10 \text{ m}$ and is brought to rest after penetrating $10 \text{ cm}$ into sand. The average force exerted by sand on the ball is . . . . . . $\text{N}$. (Take $g = 10 \text{ m/s}^2$)