$A$ 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 $g$,and if the lift moves up with a constant velocity of $2 \, m/s$,the reading on the balance will be ......... $kg$.

In the given arrangement,all surfaces are smooth. What acceleration $a$ should be given to the system (block $M$) so that the block $m_2$ does not slide down?

$A$ block is kept on a frictionless inclined surface with an angle of inclination '$\alpha$'. The incline is given a horizontal acceleration '$a$' to keep the block stationary relative to the incline. Then '$a$' is equal to:

Three masses $M = 100 \, kg$,$m_{1} = 10 \, kg$,and $m_{2} = 20 \, kg$ are arranged in a system as shown in the figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. $A$ force $F$ is applied on the system so that the mass $m_{2}$ moves upward with an acceleration of $2 \, m/s^{2}$. The value of $F$ is $...... \, N$. (Take $g = 10 \, m/s^{2}$)

$A$ circular table is rotating with an angular velocity of $\omega \text{ rad/s}$ about its axis (see figure). There is a smooth groove along a radial direction on the table. $A$ steel ball is gently placed at a distance of $1 \text{ m}$ on the groove. All the surfaces are smooth. If the radius of the table is $3 \text{ m}$,the radial velocity of the ball with respect to the table at the time the ball leaves the table is $x \sqrt{2} \omega \text{ m/s}$,where the value of $x$ is............

In an elevator moving vertically up with an acceleration $g$,the force exerted on the floor by a passenger of mass $M$ is