Two bodies $A$ and $B$ of masses $2m$ and $m$ are projected vertically upwards from the ground with velocities $u$ and $2u$ respectively. The ratio of the kinetic energy of body $A$ and the potential energy of body $B$ at a height equal to half of the maximum height reached by body $A$ is (in $ : 1$)

$A$ block of mass $5 \,kg$ is moved by a distance of $10 \,m$ on a surface with a coefficient of friction $\mu = 0.2$ by applying a force of $25 \,N$. The kinetic energy gained by the block is ...... $J$. (Take $g = 10 \,m/s^2$)

$A$ bullet of mass $m_1$ is moving with speed $v_0$ and hits a sand bag of mass $m_2$. If the speed of the bullet after passing through the sand bag is $\frac{v_0}{3}$,then the height $h$ up to which the bag rises is (assume,$g=$ acceleration due to gravity).

$A$ body of mass $10 \, kg$ at rest is acted upon simultaneously by two forces $4 \, N$ and $3 \, N$ at right angles to each other. The kinetic energy of the body at the end of $10 \, s$ is .............. $J$.

Identify the type of collision for the following cases:
$(a)$ Collision between a negatively charged object and a positively charged object.
$(b)$ Collision between two very large objects.
$(c)$ Collision between two quartz balls.

$A$ sphere of mass $m$ slides down a smooth inclined plane from a point $B$ at a height of $h$ starting from rest. The magnitude of the change in momentum of the particle between position $A$ (at the bottom of the incline) and $C$ (on the horizontal surface) is (assuming the angle of inclination of the plane is $\theta$ with respect to the horizontal):