$A$ spring balance is attached to the ceiling of a lift. $A$ man hangs his bag on the spring and the spring balance reads $49 \,N$, when the lift is stationary. If the lift moves downward with an acceleration of $5 \,m/s^2$, the reading of the spring balance will be $(g = 9.8 \,m/s^2)$. (in $\,N$)

The free surface of oil in a tanker,at rest,is horizontal. If the tanker starts accelerating,the free surface will be tilted by an angle $\theta$. If the acceleration is $a \ m/s^2$,what will be the slope of the free surface?

$A$ 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:

$A$ rocket is moving in a gravity-free space with a constant acceleration of $2 \ ms^{-2}$ along the $+x$ direction (see figure). The length of a chamber inside the rocket is $4 \ m$. $A$ ball is thrown from the left end of the chamber in the $+x$ direction with a speed of $0.3 \ ms^{-1}$ relative to the rocket. At the same time,another ball is thrown in the $-x$ direction with a speed of $0.2 \ ms^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is:

$A$ boy of $50 \, kg$ is in a lift moving down with an acceleration of $9.8 \, m/s^2$. The apparent weight of the boy is ........... $N$ $(g = 9.8 \, m/s^2)$.

$A$ man is standing in a lift which goes up and comes down with the same constant acceleration. If the ratio of the apparent weights in the two cases is $2 : 1$,then the acceleration of the lift is ......... $m/s^2$.