$A$ ball of mass $2 \,kg$ is thrown from a tall building with velocity $v = (20 \,m/s) \hat{i} + (24 \,m/s) \hat{j}$ at time $t = 0 \,s$. The change in the potential energy of the ball after $t = 8 \,s$ is (The ball is assumed to be in air during its motion between $0 \,s$ and $8 \,s$, $\hat{i}$ is along the horizontal and $\hat{j}$ is along the vertical direction. Take $g = 10 \,m/s^2$). (in $\,kJ$)

Consider the following statements $A$ and $B$. Identify the correct choice in the given answers.
$A$. In an inelastic collision,there is no loss in kinetic energy during collision.
$B$. During a collision,the linear momentum of the entire system of particles is conserved if there is no external force acting on the system.

Answer the following:
$(a)$ The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?
$(b)$ Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet's velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why?
$(c)$ An artificial satellite orbiting the earth in a very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance,however small. Why then does its speed increase progressively as it comes closer and closer to the earth?
$(d)$ In Figure $(i)$ the man walks $2\; m$ carrying a mass of $15\; kg$ on his hands. In Figure $(ii)$,he walks the same distance pulling the rope behind him. The rope goes over a pulley,and a mass of $15\; kg$ hangs at its other end. In which case is the work done greater?

Two bodies of masses $m_{1}$ and $m_{2}$ are acted upon by a constant force $F$ for a time $t$. They start from rest and acquire kinetic energies,$E_{1}$ and $E_{2}$ respectively. Then $\frac{E_{1}}{E_{2}}$ is

Consider a frictionless ramp on which a smooth object is made to slide down from an initial height $h$. The distance $d$ necessary to stop the object on a flat track (of coefficient of friction $\mu$), kept at the ramp end, is:

$A$ block of mass $m$ starts at rest at height $h$ on a frictionless inclined plane. The block slides down the plane,travels across a rough horizontal surface with coefficient of kinetic friction $\mu$,and compresses a spring with force constant $k$ a distance $x$ before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface,sliding up the plane. The block travels a total distance $d$ on the rough horizontal surface. The correct expression for the maximum height $h'$ that the block reaches on its return is