$A$ person of mass $50 \, kg$ stands on a weighing scale in a lift. If the lift is descending with a downward acceleration of $9 \, m/s^2$,what would be the reading of the weighing scale (in $, kg$)? (Take $g = 10 \, m/s^2$)

$A$ rectangular box contains water. It is being pulled to the right with an acceleration $a$. Which of the following options shows the correct shape of the water surface?

$A$ block of mass $m$ is in contact with the cart $C$ as shown in the figure. The coefficient of static friction between the block and the cart is $\mu$. The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies:

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

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.

$A$ simple pendulum is set up in a trolley which moves to the right with an acceleration $a$ on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\theta$ with the vertical.