Rotational Motion

A uniform $\operatorname{rod} A B$ is suspended from a point $P$ ，at a variable distance $x$ ，from $A$ ，as shown in figure． To make the rod horizontal，a mass＇$m$＇is suspended from its end $A$ ．Which set of variables will give a straight lin...

The moment of inertia of a thin disc about axes $a, b, c, d$ are $\mathbf{I}_1, \mathbf{I}_2, \mathbf{I}_3$ and $\mathbf{I}_4$ respectively，as shown in figure．If the moment of inertia about an axis passing through the centre and perpendicul...

The position vector of a particle of mass \(\mathrm{m}\) moving with a constant velocity \(\vec{v}\) is given by \(\vec{r}=x(t) \hat{i}+b \hat{j}\), where \(\mathrm{b}\) is a constant. At an instant, \(\vec{r}\) makes an angle \(\theta\) wi...

A small ball of mass m is suspended from the ceiling of a floor by a string of length \(\mathrm{L}\). The ball moves along a horizontal circle with constant angular velocity \(\omega\), as shown in the figure. The torque about the centre (...

A small sphere of mass m and radius r slides down the smooth surface of a large hemispherical bowl of radius R. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point \(\mathrm{A}\) of the bowl wi...

A mouse of mass m jumps on the outside edge of a rotating ceiling fan of moment of inertia I and radius R. The fractional loss of angular velocity of the fan as a result is,

A uniform rod of length L pivoted at one end P is freely rotated in a horizontal plane with an angular velocity \(\omega\) about a vertical axis passing through P. If the temperature of the system is increased by \(\Delta\)T, angular veloci...

A simple pendulum of length l is displaced, so that its taught string is horizontal and then released. A uniform bar pivoted at one end is simultaneously released from its horizontal position. If their motions are synchronous, what is the l...

Two metallic spheres of equal outer radii are found to have same moment of inertia about their respective diameters. Then, which of the following statement(s) is/are true?

Two point objects of masses 1.5 g and 2.5 g respectively are at a distance of 16 cm apart, the centre of gravity is at a distance x from the object of mass 1.5 gm where x is