System of particles practice · Medium

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

Assertion A : An electric fan continues to rotate for some time after the current is switched off.

Reason R: Fan continues to rotate due to inertia of motion.

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

Assertion: A solid sphere and a hollow sphere are rolling on ground with same total kinetic energies. If translational kinetic energy of solid sphere is $K$, then translational kinetic energy of hollow sphere should be greater than $K$.


Reason: In case of hollow sphere rotational kinetic energy is less than its translational kinetic energy.

What remains constant in the field of central force

A particle covers equal distances around a circular path in equal intervals of time. It has uniform nonzero rate of change of

A particle performing uniform circular motion has

A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of this sphere

A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be:

A circular disc is rotating about its natural axis with
angular velocity of 20 rad/s. A second disc of same
mass gently placed on it co-axially. If the radius of
disc is half of the radius of the first, then they will
start rotating with angular velocity of

If the net external forces acting on the system of particles is zero, then which of the following may vary?

A sphere is rotating about a diameter with constant angular acceleration $\alpha.$
Assertion (A): All the particles on the surface have same linear acceleration.
Reason (R): All the particles on the surface have same linear speed.

Angular momentum is

The moment of inertia of a circular ring of radius $15 \mathrm{~cm}$ and mass $150 \mathrm{~g}$ is _____

A binary star consists of two stars A (mass 2.2 ${M_s}$) and B (mass 11 ${M_s}$), where ${M_s}$ is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is

The moment of inertia of a body about a given axis is $2.4\,kg - {m^2}$. To produce a rotational kinetic energy of 750 J, an angular acceleration of 5 rad/${s^2}$ must be applied about the axis for

If the equation for the displacement of a particle moving on a circular path is given by $\left( \theta \right) = 2{t^3} + 0.5$, where $\theta$ is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is

For a body rolling along a level surface, the translational and rotational K.E are equal. The body is

Which of the following statements are correct?

1) Centre of mass of body always coincides with the centre of gravity of the body.

2) Central mass of a body is the point at which the total gravitational torque on the body is zero.

3) A couple on a body produce both translational and rotational motion in a body.

4) Mechanical advantage greater than one means that small effort can be used to lift a large load.

Two rods each having length $l$ and mass $\mathrm{m}$ joined together at point $\mathrm{B}$ as shown in figure. Then find out moment of inertia about axis passing through $\mathrm{A}$ and perpendicular to the plane of page as shown in figure.

A solid sphere of radius $R$ has its outer half removed, so that its radius becomes $(R / 2)$. Then its moment of inertia about the diameter is

The velocity of a solid sphere on reaching the bottom of an inclined plane is $v^{\prime}$ when it slides down. The value of $v / v^{\prime}$ will be

A man of 50 kg mass in standing in a gravity free space at a height of 10m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2m/s. When the stone reaches the floor, the distance of the man above the floor will be

A smooth sphere $A$ is moving on a frictionless horizontal plane with angular speed $\omega$ and centre of mass velocity $v$. It collides elastically and head on with an identical sphere $B$ at rest. Neglect friction everywhere. After the collision, their angular speeds are $\omega_A$ and $\omega_B$, respectively. Then

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

A flywheel is making $3000 / \pi$ revolutions per minute about its axis. If the moment of inertia of the flywheel about that axis is $400 \,\mathrm{kgm}^2$, its rotational kinetic energy is

Assertion: There is a line passing through the tangent of a disc; the disc's moment of inertia about that line is $\frac{7}{4} M R^2$

Reason: If the disc's moment of inertia about its diameter is known then to know the moment of inertia about the tangent line, we need to use the parallel axis theorem.

Assertion: If a person jumps from a height with his legs rigid, then his ankle is more injured.
Reason: The force will be maximum on its ankle during the collision with ground.

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is

What is moment of inertia in terms of angular momentum (L) and kinetic energy (K)?

Statement I: The centre of mass of a circular disc lies always at the centre of the disc.

Statement II: Circular disc is a symmetrical body.

If ' $I$ ' is the moment of inertia and ' $L$ ' is angular momentum of a rotating body, then $\frac{L^2}{2 I}$ is its