List of top Physics Questions on Rotational Mechanics

A uniform solid cylinder of length $L$ and radius $R$ has moment of inertia about its axis equal to $I_1$. A small co-centric cylinder of length $L/2$ and radius $R/3$ carved from it has moment of inertia about its axis equal to $I_2$. The ratio $I_1/I_2$ is ________.

A thin uniform rod ($X$) of mass $M$ and length $L$ is pivoted at a height $ \left(\dfrac{L}{3}\right) $ as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top is ________. ($g$ = gravitational acceleration)

In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$)

Two masses $400\,\text{g}$ and $350\,\text{g}$ are suspended from the ends of a light string passing over a heavy pulley of radius $2\,\text{cm}$. When released from rest the heavier mass is observed to fall $81\,\text{cm}$ in $9\,\text{s}$. The rotational inertia of the pulley is ___ $\text{kg m}^2$.
(Given: $g = 9.8\,\text{m s}^{-2}$)

A uniform bar of length $12\,\text{cm}$ and mass $20m$ lies on a smooth horizontal table. Two point masses $m$ and $2m$ are moving in opposite directions with the same speed $v$ and in the same plane as the bar, as shown in the figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $\omega$. The ratio of $v$ and $\omega$ is

A conducting circular loop is rotated about its diameter at a constant angular speed of $100 \, \text{rad s}^{-1}$ in a magnetic field of $0.5 \, \text{T}$, perpendicular to the axis of rotation. When the loop is rotated by $30^\circ$ from the horizontal position, the induced EMF is $15.4 \, \text{mV}$. The radius of the loop is ______________ mm.
(Take $ \pi = \dfrac{22}{7} $)

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma = 10$ mho/m. The ratio of maximum conduction current density to maximum displacement current density is _________.
$\left[ \text{Take } \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2 \right]$

A capacitor $C$ is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance $L$. In $t$ s 25% of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is _________ s.

Two known resistances of $R \Omega$ and $2R \Omega$ and one unknown resistance $X \Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points $A$ and $B$ in the circuit is $X \Omega$, then the value of $X$ is _________ $\Omega$.

After release, the blocks moves 81 cm in 9 seconds. Find moment of inertia of the pulley :
(Given $m_{1} = 400$ gm, $m_{2} = 350$ gm, R = 2 cm, g = 10 m/s$^2$)

Block of mass $3\,\text{kg}$ is connected to a flywheel of mass $3\,\text{kg}$ and radius $5\,\text{m}$ through a massless string wrapped around the flywheel. Find kinetic energy (in J) of flywheel when block descends by $3\,\text{m}$.

In the system of two discs and a rod of mass 600 g each, a torque of magnitude $43 \times 10^5$ dyne-cm is applied along the axis of rotation as shown in figure. Find the approx angular acceleration about given axis :

Two discs have the same moment of inertia about their axis. Their thicknesses are $t_1$ and $t_2$ and they have the same density. If $ \dfrac{R_1}{R_2} = \dfrac{1}{2} $, find $ \dfrac{t_1}{t_2} $.

Disk $ m_1 = 5 \, \text{kg} $ \& radius $ r_1 = 10 \, \text{cm} $ and disk $ m_2 = 10 \, \text{kg} $ \& radius $ r_2 = 50 \, \text{cm} $ are arranged as shown in the figure. Find the moment of inertia about an axis through the common tangent and parallel to the plane of the disks.

All are cylindrical rods having radius of cross-section $R$ and mass of each rod $\dfrac{M}{4}$. Find the moment of inertia about $yy'$ axis:

Masses $m$ and $2m$ are connected by a massless rod of length $d$. If angular momentum about an axis passing through centre of mass and perpendicular to the rod is $L$, then the angular speed $(\omega)$ of the system is: