System of particles practice · Mixed difficulty

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

If a force $10\hat i + 15\hat j + 25\hat k$ acts on a system and gives an acceleration $2\hat i + 3\hat j - 5\hat k$ to the centre of mass of the system, the mass of the system is

A thin uniform circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity $\omega$. Another disc of same thickness and radius but of mass $\frac{1}{8} \mathrm{M}$ is placed gently on the first disc co-axially. The angular velocity of the system is now

A uniform disc of radius $a$ and mass $m$ is rotating freely with angular speed $\omega$ in a horizontal plane about a smooth fixed vertical axis through its centre. A particle of mass $m$ is suddenly attached to the rim of the disc and rotates with it. The new angular speed is

A dancer on ice spins faster when she folds her arms. This is due to

If F^ → = 2 \widehat i - 3\widehat j N$\mathop \mathrm{F}\limits^ \to = 2\,\widehat \mathrm{i} - 3\widehat \mathrm{j}\,\,\mathrm{N}$ and r^ → = 3 \widehat i + 2\widehat j m$\mathop r\limits^ \to = 3\,\widehat \mathrm{i} + 2\widehat \mathrm{j}\,\,m$ then torque $\overrightarrow \tau$ is

A particle is moving with uniform speed $0.5\,m/s$ along a circle of radius $1m$, then the angular velocity of particle is ( in $rad{s^{ - 1}}$)

A car is accelerating on a rough horizontal track. The wheels are rolling purely.
Statement-1: Friction does positive work on car.
Statement-2: The friction force is responsible for the acceleration of the car on a rough horizontal track.

(A): The size and shape of the rigid body remains unaffected under the effect of extemal forces.
(R): The distance between two particles remains constant in a rigid body.

Select incorrect statement

A uniform disc of mass 2 kg and radius 15 cm is revolving around the central axis by 4 $\mathrm{rad}{\mathrm{s}^{ - 1}}$. The linear momentum of disc will be

A coin is of mass 4.8 kg and radius one metre rolling on a horizontal surface without sliding with angular velocity 600 rotation/min. What is total kinetic energy of the coin ?

The motion of the centre of mass is the result of

If we hollow the ball of pendulum and fill it with sand, what would be the effect of change on the center of mass?

A solid sphere rolls down without slipping from rest on an $\mathrm{3}{\mathrm{0}^0}$ incline. Its linear acceleration is

One quarter of the disc of mass m is removed. If $r$ be the radius of the disc, the new moment of inertia is

Assertion: The centre of mass of a body may lie outside the body.
Reason: The centre of mass of a body depends on the distribution of mass in the body.

A ballet dancer suddenly folds her outstretched
arms. Her angular velocity

If the earth were to contract such that its
radius becomes one quarter, without change in
its mass, the duration of one full day would be

A flywheel is in the form of solid circular wheel of mass 72 kg and radius of 0.5m and it takes 70 r.p.m, then the energy of revolution is