$A$ solid sphere,a hollow sphere,and a ring are released from the top of an inclined plane (frictionless) so that they slide down the plane. Then,the maximum acceleration down the plane is for (no rolling):

$A$ frictionless wire $AB$ is fixed on a circle of radius $R$. $A$ very small bead slips on this wire. The time taken by the bead to slip from $A$ to $B$ is:

For the given system, the acceleration of the system is ........... $ms^{-2}$ $(\sin 37^\circ = 0.60, \sin 53^\circ = 0.80)$.

Block $A$ of weight $100 \, N$ rests on a frictionless inclined plane of slope angle $30^{\circ}$. $A$ flexible cord attached to $A$ passes over a frictionless pulley and is connected to block $B$ of weight $w$. Find the weight $w$ for which the system is in equilibrium.

As shown in the figure,two spheres are released from point $A$ along paths $AB$ and $AC$ respectively. If both surfaces are smooth,find the time taken by both spheres to reach the bottom of the incline. (Take $g = 10 \, m/s^2$)

The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane $9.8 \ m$ long (angle of inclination is $30^o$) is ......... $sec$.