Consider the following statements $A$ and $B$ and identify the correct answer given below:
$(A)$ $A$ body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time.
$(B)$ When a body is at rest, it must be in equilibrium.

$A$ vehicle is moving with uniform speed along $3$ different shaped roads: horizontal,concave,and convex. The surface of the road on which the normal reaction on the vehicle is maximum is

$A$ balloon of mass $m$ is descending down with an acceleration $\frac{g}{2}$. How much mass should be removed from it so that it starts moving up with the same acceleration?

$A$ metal block is resting on a rough wooden surface. $A$ horizontal force applied to the block is increased uniformly with time,i.e.,$F = kt$. Which of the following curves correctly represents the velocity $v$ of the block as a function of time $t$?

In the figure,two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with coefficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall. The pulley is frictionless. Imagine a situation in which the given arrangement is placed inside an elevator that can move only in the vertical direction and compare the situation with the case when it is placed on the ground. When the elevator accelerates downward with $a_0 (< g)$,then

$A$ cubical box of side $a$ sitting on a rough table-top is pushed horizontally with a gradually increasing force until the box moves. If the force is applied at a height from the table top which is greater than a critical height $H$,the box topples first. If it is applied at a height less than $H$,the box starts sliding first. Then,the coefficient of friction between the box and the table top is