The ratio of the weight of a man in a stationary lift and when it is moving downward with uniform acceleration $a$ is $3 : 2$. The value of $a$ is ($g$ = acceleration due to gravity of the earth).

$A$ man of mass $70 \; kg$ stands on a weighing scale in a lift which is moving:
$(a)$ Upwards with a uniform speed of $10 \; m s^{-1}$.
$(b)$ Downwards with a uniform acceleration of $5 \; m s^{-2}$.
$(c)$ Upwards with a uniform acceleration of $5 \; m s^{-2}$.
What would be the readings on the scale in each case?
$(d)$ What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

In the figure shown,$P$ is a plate on which a wedge $B$ is placed,and on $B$ a block $A$ of mass $m$ is placed. The plate is suddenly removed and the system of $B$ and $A$ is allowed to fall under gravity. Neglecting any force due to air on $A$ and $B$,the normal force on $A$ due to $B$ is

The free surface of oil in a tanker,at rest,is horizontal. If the tanker starts accelerating,the free surface will be tilted by an angle $\theta$. If the acceleration is $a \ m/s^2$,what will be the slope of the free surface?

$A$ man of mass $80\, kg$ is standing in an elevator which is moving with an acceleration of $6\, m/s^2$ in the upward direction. The apparent weight of the man will be ......... $N$ $(g = 10\, m/s^2)$.

$A$ box of mass $m \, kg$ is placed on the rear side of an open truck accelerating at $4 \, m/s^2$. The coefficient of friction between the box and the surface below it is $0.4$. The net acceleration of the box with respect to the truck is zero. The value of $m$ is :- $[g = 10 \, m/s^2]$