$A$ trolley is sliding freely down an inclined plane as shown in the figure. The angle $(\alpha)$ that the string of the pendulum makes with the ceiling of the trolley is equal to ..........

Three weights $W, 2W$,and $3W$ are connected to identical springs suspended from a rigid horizontal rod. The assembly of the rod and the weights falls freely under gravity. The positions of the weights from the rod are such that:

$A$ plank is moving in a horizontal direction with a constant acceleration $a \hat{i}$. $A$ uniform rough cubical block of side $l$ rests on the plank and is at rest relative to the plank. Let the centre of mass of the block be at $(0, l/2)$ at a given instant. If $a = g/10$,then the normal reaction exerted by the plank on the block at that instant acts at

The spring balance inside a lift suspends an object. As the lift begins to ascend,the reading indicated by the spring balance will

In an elevator moving vertically up with an acceleration $g$,the force exerted on the floor by a passenger of mass $M$ is

$A$ body of mass $1.0 \, kg$ is falling with an acceleration of $10 \, m/s^2$. Its apparent weight will be ......... $kg \, wt$ $(g = 10 \, m/s^2)$.