$A$ man of weight $mg$ is in a lift moving up with an acceleration of $4g$. The apparent weight of the man in the lift is:

$A$ person sitting inside an elevator performs a weighing experiment with an object of mass $50 \ kg$. Suppose that the variation of the height $y$ (in $m$) of the elevator,from the ground,with time $t$ (in $s$) is given by $y = 8[1 + \sin(\frac{2 \pi t}{T})]$,where $T = 40 \pi \ s$. Taking acceleration due to gravity,$g = 10 \ m/s^2$,the maximum variation of the object's weight (in $N$) as observed in the experiment is $.....$ .

The apparent weight of a body,when it is travelling upwards with an acceleration of $2 \ m/s^2$ and its mass is $10 \ kg$,will be ......... $N$.

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

Two wooden blocks of masses $M$ and $m$ are placed on a smooth horizontal surface as shown in the figure. If a force $P$ is applied to the system as shown in the figure such that the mass $m$ remains stationary with respect to the block of mass $M$,then the magnitude of the force $P$ is

$A$ mass $M$ is placed on a smooth wedge of angle $\theta$ resting on a frictionless surface. To keep the mass $M$ at rest relative to the wedge,the wedge must be given a horizontal acceleration $a$ equal to: