$A$ simple pendulum is set up in a trolley which moves to the right with an acceleration $a$ on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\theta$ with the vertical.

$A$ piece of wire is bent in the shape of a parabola $y=kx^2$ ($y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $a$. The distance of the new equilibrium position of the bead,where the bead can stay at rest with respect to the wire,from the $y$-axis is

$A$ thief stole a box full of valuable articles of weight $W$ and while carrying it on his back,he jumped down a wall of height $h$ from the ground. Before he reached the ground,he experienced a load of:

$A$ lift is moving down with an acceleration $a$. $A$ man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively:

You stand on a spring scale on the floor of an elevator. Of the following,the scale shows the highest reading when the elevator

The ratio of the weight of a man in a stationary lift to his weight in a lift moving downwards with an acceleration '$a$' is $3:2$. Then '$a$' = . . . . . . .