$A$ 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 of mass $80\, kg$ is standing in an elevator which is moving with an acceleration of $6\, m/s^2$ in the upward direction. The apparent weight of the man will be ......... $N$ $(g = 10\, m/s^2)$.

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:

$A$ 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:

$A$ block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be

$A$ person is standing in an elevator. In which situation does he experience weight loss?