$A$ small sphere is moving at $a$ constant speed in $a$ vertical circle. Below is a list of quantities that could be used to describe some aspect of the motion of the sphere.

$I$ - kinetic energy

$II$- gravitational potential energy

$III$ - momentum

Which of these quantities will change as this sphere moves around the circle?

A body of mass $50\, kg$ is projected vertically upwards with velocity of $100 \,m/sec$. $5 \,seconds$ after this body breaks into $20\, kg$ and $30 \,kg$. If $20\, kg $ piece travels upwards with $150 \,m/sec$, then the velocity of other block will be

A particle of mass $m$ with initial kinetics energy $K$ approaches the origin from $x =+\infty$. Assume that a conservative force acts on it and its potential energy $V ( x )$ is given by $V ( x )=\frac{ K }{\exp \left(3 x / x _0\right)+\exp \left(-3 x / x _0\right)}$ where, $x_0=1 m$. The speed of the particle at $x =0$ is

An object flying in alr with velocity $(20 \hat{\mathrm{i}}+25 \hat{\mathrm{j}}-12 \hat{\mathrm{k}})$ suddenly breaks in two pleces whose masses are in the ratio $1: 5 .$ The smaller mass flies off with a velocity $(100 \hat{\mathrm{i}}+35 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}) .$ The velocity of larger piece will be

An isolated rail car of mass $M$ is moving along a straight, frictionless track at an initial speed $v_0$. The car is passing under a bridge when $a$ crate filled with $N$ bowling balls, each of mass $m$, is dropped from the bridge into the bed of the rail car. The crate splits open and the bowling balls bounce around inside the rail car, but none of them fall out. What is the average speed of the rail car $+$ bowling balls system some time after the collision?

Two particles of masses $m_1, m_2$ move with initial velocities $u_1$and $u_2$ On collision, one of the particles get excited to higher level, after absorbing energy $\varepsilon $. If final velocities of particles be $v_1$ and $v_2$ then we must have