List of top Physics Questions on rotational motion

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is $\sqrt\frac{8} {x }$. The value of x is:

A coin is placed on a disc. The coefficient of friction between the coin and the disc is $ \mu $. If the distance of the coin from the center of the disc is $ r $, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is:

A circular disc reaches from top to bottom of an inclined plane of length $ l $. When it slips down the plane, it takes $ t $ s. When it rolls down the plane, then it takes \[ \left( \frac{\alpha}{2} \right)^{1/2} t \, \text{s}, \] where $ \alpha $ is __________ .

Two discs of moment of inertia $ I_1 = 4 \, kg \, m^2 $ and $ I_2 = 2 \, kg \, m^2 $ about their central axes and normal to their planes, rotating with angular speeds $ 10 \, rad/s $ and $ 4 \, rad/s $ respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is __________ J.

A solid sphere and a hollow cylinder roll up without slipping on the same inclined plane with the same initial speed $ v $. The sphere and the cylinder reach up to maximum heights $ h_1 $ and $ h_2 $, respectively, above the initial level. The ratio $ h_1 : h_2 $ is $ \frac{n}{10} $. The value of $ n $ is ______.

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $ \frac{7}{x} $ where $ x $ is $\_\_\_\_\_\_\_$.

Four particles each of mass 1 kg are placed at four corners of a square of side 2 m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertices is _____ kgm².

A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve radius of 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, $ g = 10 \, \text{m/s}^2 $):

Consider a disc of mass 5 kg, radius 2 m, rotating with angular velocity of 10 rad/s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is $ \_\_\_\_ $ J.

A cylinder is rolling down an inclined plane of inclination $ 60^\circ $. Its acceleration during rolling down will be $ \frac{x}{\sqrt{3}} \, \text{m/s}^2 $, where $ x = $ _____. (Use $ g = 10 \, \text{m/s}^2 $).

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be √x m. The value of x is _______ .

A bar of m = 1.00 kg and length l = 0.20 m is lying on a horizontal frictionless surface. One end of the bar is pivoted so that the bar is free to rotate in the vertical plane. a small m = 0.10 kg is moving on the same horizontal surface with 5.00 ms^-1 speed on its path which is perpendicular to the bar. Its hits the bar at a distance $\frac{L}{2}$ from the pivoted end and return back on the same path with speed v. After this elastic collision, the bar rotates with an angular velocity ω. Which of the following statement is correct?

The figure represents the momentum time (p-t) curve for a particle moving along an axis under the influence of the force Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ?If $\left(t_3-t_2\right) < t_1$

An object of mass $8 kg$ is hanging from one end of a uniform rod CD of mass $2 kg$ and length $1 m$ pivoted at its end $C$ on a vertical wall as shown in figure It is supported by a cable $AB$ such that the system is in equilibrium The tension in the cable is : (Take $g =10 m / s ^2$ )

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R
Assertion (A):- fan spins even after switch is off
Reason (R):- Fan in rotation has rotational inertia.
In the light of the above statements, choose the correct answer from the options given belows

A uniform disc of mass $0.5\, kg$ and radius $r$ is projected with velocity $18 \,m / s$ at $t=0$ s on a rough horizontal surface It starts off with a purely sliding motion at $t=0\, s$ After $2\, s$ it acquires a purely rolling motion (see figure) The total kinetic energy of the disc after $2 \,s$ will be ______ $J$ (given, coefficient of friction is $0.3$ and g=10m/s²⁾

A thin uniform rod of length $2 m$, cross sectional area ' $A$ ' and density ' $d$ ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$ If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha Ad }{ Ad }}$ then value of $\alpha$ is _____

A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ $ms ^{-1}$(Given $g =10 \,ms ^{-2}$ )

A thin uniform rod of length $2 m$, cross sectional area ' $A$ ' and density ' $d$ ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$ If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha Ad }{ Ad }}$ then value of $\alpha$ is _____

The ratio of the radii of two solid spheres of same mass in 2:3. The ratio of the moments of inertia of the spheres about their diameters is:

A thin circular coin of mass 5 gm and radius $\frac{4}{3}$ is initially in a horizontal XY - plane. The coin is tossed vertically up (+Z direction) by applying an impulse of $\sqrt{\frac{\pi}{2}\times10^{-2}}$ N-s at a distance of $\frac{2}{3}$ cm from its center. The coin spins about its diameter and moves along the +𝑧 direction. By the time the coin reaches back to its initial position, it completes 𝑛 rotations. The value of 𝑛 is ____. [Given: The acceleration due to gravity 𝑔 = 10 ms⁻²]

Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is __________ × 10^{-3} kg-m^2

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

An annular disk of mass 𝑀, inner radius 𝑎 and outer radius 𝑏 is placed on a horizontal surface with coefficient of friction 𝜇, as shown in the figure. At some time, an impulse ℐ₀𝑥̂ is applied at a height ℎ above the center of the disk. If ℎ = ℎ𝑚 then the disk rolls without slipping along the 𝑥-axis.Which of the following statement(s) is(are) correct?

A thin circular coin of mass 5 gm and radius $\frac{4}{3}$ is initially in a horizontal XY - plane. The coin is tossed vertically up (+Z direction) by applying an impulse of $\sqrt{\frac{\pi}{2}\times10^{-2}}$ N-s at a distance of $\frac{2}{3}$ cm from its center. The coin spins about its diameter and moves along the +𝑧 direction. By the time the coin reaches back to its initial position, it completes 𝑛 rotations. The value of 𝑛 is ____. [Given: The acceleration due to gravity 𝑔 = 10 ms⁻²]

List of top Physics Questions on rotational motion

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