$A$ body of mass $5 \ kg$ is suspended by a spring balance on an inclined plane as shown in the figure. The spring balance measures (in $N$):

$A$ frictionless wire $AB$ is fixed on a sphere of radius $R$. $A$ very small spherical ball slips on this wire. The time taken by this ball to slip from $A$ to $B$ is

$A$ body starts falling freely from height $H$ and hits an inclined plane in its path at height $h$ from the ground. As a result of this perfectly elastic impact,the direction of the velocity of the body becomes horizontal. The value of $\frac{H}{h}$ for which the body will take the maximum time to reach the ground is . . . . . . .

Two wooden blocks are moving on a smooth horizontal surface such that the block of mass $m$ remains stationary with respect to the block of mass $M$ as shown in the figure. The magnitude of force $P$ is:

The horizontal acceleration that should be given to a smooth inclined plane of angle $\sin^{-1} (1/l)$ to keep an object stationary on the plane relative to the inclined plane is

$A$ block of mass $m$ is released from rest at point $A$ on an inclined plane of angle $\theta$ with the vertical. The block slides down and compresses a spring of spring constant $k$. Find the compression in the spring when the speed of the block is maximum.