$A$ 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 ....... $kg$.

In the figure,the reading of the spring balance will be $......\,N$ $\left[ g = 10\,m/s^2 \right]$.

The horizontal acceleration that should be given to a smooth inclined plane of angle $\theta = \sin^{-1}\left(\frac{1}{l}\right)$ to keep an object stationary on the plane,relative to the inclined plane is:

$A$ person in an elevator accelerating upwards with an acceleration of $2 \, m/s^2$ tosses a coin vertically upwards with a speed of $20 \, m/s$. After how much time will the coin fall back into his hand (in $, s$)? $(g = 10 \, m/s^2)$

An object of mass $2 \, kg$ is placed at rest in a frame $S_1$ moving with velocity $10 \hat{i} + 5 \hat{j} \, m/s$ and having acceleration $5 \hat{i} + 10 \hat{j} \, m/s^2$. The object is also seen by an observer standing in a frame $S_2$ moving with velocity $5 \hat{i} + 10 \hat{j} \, m/s$. Calculate the net force acting on the object with respect to the $S_2$ frame.

$A$ 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 $N$)