$A$ point mass $m$ is suspended from a light thread of length $l$,fixed at $O$,and is whirled in a horizontal circle at a constant speed as shown. From your point of view,stationary with respect to the mass,the forces on the mass are

An object of mass $2 \, kg$ is placed at rest in a frame $S_1$ moving with velocity $10 \hat{i} + 5 \hat{j} \, m/s$ and having acceleration $5 \hat{i} + 10 \hat{j} \, m/s^2$. The object is also seen by an observer standing in a frame $S_2$ moving with velocity $5 \hat{i} + 10 \hat{j} \, m/s$. Calculate the net force acting on the object with respect to the $S_2$ frame.

$A$ cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with an acceleration $a$ downwards, the length of the spring:

$A$ 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

$A$ person is standing in an elevator. In which of the following situations does he find his weight to be less than his actual weight?

$A$ car is moving with a uniform speed on a level road. Inside the car,there is a balloon filled with helium and attached to a piece of string tied to the floor. The string is observed to be vertical. The car now takes a left turn while maintaining the same speed on the level road. The balloon in the car will: