Two bodies of masses $m_1$ and $m_2$ are connected by a light string which passes over a frictionless,massless pulley. If the pulley is moving upward with uniform acceleration $\frac{g}{2}$,then the tension in the string will be .........

$A$ wooden block of mass $5 \, kg$ rests on a soft horizontal floor. When an iron cylinder of mass $25 \, kg$ is placed on top of the block, the floor yields and the block and the cylinder together move down with an acceleration of $0.1 \, m/s^2$. The action force of the system on the floor is equal to: (in $N$)

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

$A$ 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 :- $[g = 10 \, m/s^2]$

$A$ body of mass $2 \, kg$ is hung on a spring balance mounted vertically in a lift. If the lift descends with an acceleration equal to the acceleration due to gravity $g$,the reading on the spring balance will be ....... $kg$.

$A$ wedge of height $H$ (fixed) and inclination $\alpha$ (variable) is moving on a smooth horizontal surface with constant acceleration $g \ m/s^2$. $A$ small block is placed at the bottom of the incline as shown in the figure, and it slips on the smooth surface of the incline. Choose the $CORRECT$ statement about the time taken by the block to reach the top of the incline.