$A$ 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:

$A$ spring balance and a physical balance are kept in a lift. In these balances,equal masses are placed. If the lift starts moving upwards with constant acceleration,then:

The mass of a person sitting in a lift is $50 \, kg$. If the lift is coming down with a constant acceleration of $10 \, m/s^2$,then the reading of the spring balance will be ......... $N$ $(g = 10 \, m/s^2)$.

$A$ man of mass $70 \; kg$ stands on a weighing scale in a lift which is moving:
$(a)$ Upwards with a uniform speed of $10 \; m s^{-1}$.
$(b)$ Downwards with a uniform acceleration of $5 \; m s^{-2}$.
$(c)$ Upwards with a uniform acceleration of $5 \; m s^{-2}$.
What would be the readings on the scale in each case?
$(d)$ What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

$A$ block can slide on a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with a retardation $a$,the acceleration of the block relative to the incline is

$A$ vessel containing water is given a constant acceleration $a$ towards the right,along a straight horizontal path. Which of the following diagrams represents the surface of the liquid?