$A$ body of mass $50 \ kg$ is suspended using a spring balance inside a lift at rest. If the lift starts falling freely,the reading of the spring balance is:

$A$ cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with an acceleration $a$ downwards, the length of the spring:

$A$ wooden wedge of mass $M$ and inclination angle $\alpha$ rests on a smooth floor. $A$ block of mass $m$ is kept on the wedge. $A$ force $F$ is applied on the wedge as shown in the figure such that the block remains stationary with respect to the wedge. The magnitude of the force $F$ 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

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: