Rotational Motion - Mechanics - Physics Previous Year Questions

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 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 will be [given, moment of inertia of sphere \(=\frac{2}{5} \mathrm{mr}^2\)]

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 \(\theta\) with the \(x\)-axis as shown in the figure. The variation of the angular momentum of the particle about the origin with \(\theta\) will be

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 (O) of the horizontal circle is

If the rotational kinetic energy of a body is increased by $300 \%$, then the percentage increase in its angular momentum will be

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

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 perpendicular to the plane of the disc is I then，

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 line when they are plotted？