As per the given figure,a weightless pulley $P$ is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if $g = 10 \, m/s^2$):

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

$A$ small block slides without friction down an inclined plane starting from rest. Let $S_n$ be the distance travelled from time $t = n - 1$ to $t = n$. Then $\frac{S_n}{S_{n+1}}$ is

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 $g = 10 \, m/s^2$)

$A$ smooth inclined plane is inclined at an angle $\theta$ with the horizontal. $A$ body starts from rest and slides down the inclined surface. The time taken by it to reach the bottom is

What should be the minimum force $P$ to be applied to the string so that a block of mass $M$ just begins to move up the frictionless inclined plane? The string passes over a pulley attached to the block,with one end fixed to the incline and the other pulled with force $P$ at an angle $\theta$ with the incline.