Rotational Motion - Mechanics - Physics Previous Year Questions

A solid cylinder of mass $m$ and radius $R$ rolls down on an inclined plane of height 30 m without slipping. The speed of its centre of mass, when the cylinder reaches the bottom is

[use $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

Moon revolves around the earth in an orbit of radius $R$ with time period of revolution $T$. It also rotates about its own axis with a time period $T$. If mass of the moon is $M$ and its radius is $r$, the total kinetic energy of the moon is

The spinning of the Diwali cracker 'ground chakkar' involves the concept of

A particle of mass $m$ is moving along a line $y=x+a$ with a constant velocity $v$. The angular momentum of the particle about the origin is

A body is rolling without slipping on a horizontal plane. If the rotational kinetic energy of the body is $50 \%$ of its total kinetic energy, then the body is

A constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4 A_0$ in 4 seconds. The magnitude of the torque is

A particle performs uniform circular motion with an angular momentum $L$. If the frequency of the particle's motion is doubled and its kinetic energy is halved, then its angular momentum becomes

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

A solid sphere and a solid cylinder, each of mass $M$ and radius $R$ are rolling with a linear speed on a flat surface without slipping. Let $L_1$ be magnitude of the angular momentum of the sphere with respect to a fixed point along the path of the sphere. Likewise $L_2$ be the magnitude of angular momentum of the cylinder with respect to the same fixed point along its path. The ratio $L_1 / L_2$ is

An object of mass 2 kg is hanging from a rope that is wrapped around a pulley of radius 25 cm . The mass of pulley is 2 kg . Find the acceleration of the object. (Assume, pulley to be a solid disk $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A metre stick is balanced on the knife edge at its centre. When four coins, each of mass 2 g are put one on top of the other at 10.0 cm mark, the stick it found to be balanced at 46.0 cm mark. The mass of the metre stick is

A wheel of radius with 0.5 m and a moment of inertia of $10 \mathrm{~kg}-\mathrm{m}^2$ is rotating freely at an angular speed of 70 $\mathrm{rev} / \mathrm{min}$. The wheel can be stopped in 5.0 s by pressing a wet cloth against the rim and exerting a radially inward force of 88 N . The coefficient of kinetic friction between the wheel and wet cloth is

A solid spherical ball is rolled up an inclined plane of angle of inclination $30^{\circ}$ with an initial speed of $4 \mathrm{~m} / \mathrm{s}$ at the bottom of the inclination. How far will the ball go up the plane?

(Use, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A solid cylinder is released from rest from the top of an inclined plane of inclination $30^{\circ}$ and length 60 cm . If the cylinder rolls without slipping, then the speed when it reaches the bottom is

Consider a thin metal strip of mass l kg and length 5 m . Calculate its moment of inertia about an axis perpendicular to strip and located at 100 cm on strip from one its end. (Assume the breadth as the strip is negligible)

A rod of length $L$ revolves in a horizontal plane about the axis passing through its centre and perpendicular to its length. The angular velocity of the rod is $\omega$. If $A$ is the area of cross-section of the rod and $\rho$ is its density, then the rotational kinetic energy of the rod is

A solid sphere of mass 2 kg rolls on a smooth horizontal surface at $10 \mathrm{~m} / \mathrm{s}$. It then rolls up a smooth inclined plane of inclination $30^{\circ}$ with the horizontal. The height attained by the sphere before it stops is [take $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

Consider a uniform horizontal solid cylinder of mass 10 kg such that its length is 9 times its radius. Let the radius be 40 cm . Calculate the moment of inertia of the cylinder about a line passing through its edge and perpendicular to its axis.

A straight rod of length $L$ is made of a material having mass per unit length $m(x)=\lambda|x|$, where $x$ is measured from the centre of rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod will be $L=1 \mathrm{~m}$ and $\lambda=16 \mathrm{~kg} / \mathrm{m}^2$.