System of particles practice · Mixed difficulty

A rope is wound around a hollow cylinder of mass
4 kg and radius 20 cm. What is the angular
acceleration of the cylinder if the rope is pulled
with a force of 15 N:

If $\alpha$ is angular acceleration, $\omega$ is angular velocity and a is the centripetal acceleration then, which of the following is true?

A thin hollow sphere of mass $m$ is completely filled with non viscous liquid of mass $m$. When the sphere roll-on horizontal ground such that centre moves with velocity $v$, kinetic energy of the system is equal to

Consider a system of two identical particles in which first one is accelerating with $2 {~m} / {s}^2$ and second one is at rest. The centre of mass of this system will have an acceleration

A body is rotating with angular velocity $\omega = \left( {3\hat i - 4\hat j - \hat k} \right)$. The linear velocity of a point having position vector $r = \left( {5\hat i - 6\hat j + 6\hat k} \right)$ is

Assertion (A): A disc is rolling on a rough horizontal surface without slipping. The velocity of centre of mass is $v .$ Then all the other points on the disc lying on a circular arc with point of contact as the center and this arc passing through center of mass of disc will have the same speed $v.$
Reason (R): When a disc is rotating without sliding on a rough horizontal surface the magnitude of velocities of all the points at a distance $r$ from point of contact is same.

Statement-1: If a rod is thrown up vertically in absence of air drag, it returns back to the ground without any change in it's angular velocity.
Statement-2: In absence of any torque, the angular momentum of system is conserved.

Moment of inertia of big drop in $I$. If 8 droplets are formed from big drop, then moment of inertia of small droplet is

Find the position of centre of mass from the base of a uniform solid cone of height $20 \mathrm{~cm}$.

A car sometimes overturns while taking a turn. When it overturns, it is

Moment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is $I$. What is the moment of inertia about its diameter

A constant torque acting on a uniform circular wheel changes its angular momentum from ${A_0}\,\,to\,\,\mathrm{ }7{A_0}$ in 3 s. The magnitude of average torque is

Analogue of mass in rotational motion is

A solid sphere of mass 500 g and radius 10 cm rolls without slipping with the velocity 20 cm/s. The total kinetic energy of the sphere will be

Statement I: Total torque on a system is independent of
the origin if the total external force is zero.
Statement II: Torque due to a couple is independent of
the origin.

Of the two eggs which have identical sizes, shapes and weights, one is raw, and other is half boiled. The ratio between the moment of inertia of the raw to the half boiled egg bout central axis is

A uniform circular disc has a radius of 20 cm. A circular disc of radius 10 cm is cut concentrically from the original disc. The shift in the centre of mass is

A cylinder of mass M, length L and radius R. If its moment of inertia about an axis passing through its centre and perpendicular to its axis is minimum, the ratio L/R must be equal to

Very thin ring of radius R is rotated about its centre. It’s radius will

If a sphere of mass 4 kg and diameter 10 cm is rolling at speed $10\,m{s^{ - 1}}$. Its rotational kinetic energy is

A uniform wire of length 6.28 cm is bent in the form of a circle. The shift in its centre of mass is

There are some passengers inside a stationary railway compartment. The centre of mass of the compartment itself (without the passengers) is $C_1,$ while the centre of mass of the 'compartment plus passengers' system is $C_2.$ If the passengers move about inside the compartment then

A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved?

A scooter is going round a circular road of radius 100 m at a speed of 10 m/s. The angular speed of the scooter will be

A ring starts from rest and acquires an angular speed of $10\mathrm{ }rad{s^{ - 1}}$ in 2s. The mass of the ring is 500 gm and its radius is 20 cm. The torque on the ring is

An isolated particle of mass m is moving in a horizontal plane (x-y), along the x-axis, at a certain height above the ground. It suddenly explodes into two fragments of masses m/4 and 3m/4. An instant later, the smaller fragment is at $y = + 15$ cm. The larger fragment at the instant is at

Given below are two statements : one is labelled as
Assertion (A) and the other is labelled as Reason
(R).

Assertion (A) : The angular speed of the moon in
its orbit about the earth is more than the angular
speed of the earth in its orbit about the sun.

Reason (R) : The moon takes less time to move
around the earth than the time taken by the earth to
move around the sun.

In the light of the above statements, choose the
most appropriate answer from the options given
below:

Two bodies of masses 3 kg and 2 kg moves with an acceleration are $2\,m{s^{ - 2}}$ and $4\,m{s^{ - 2}}.$ Find the acceleration of centre of mass in $m{s^{ - 2}}$ is

The density of a rod is increasing from end A to B it is easier to set in rotation by