System of particles practice · Medium

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

Two particles of masses $m_1$ and $m_2\left(m_1 > m_2\right)$, initially at rest, moves towards each other under an inverse square law force of attraction. Pick out the correct statement about the centre of mass (CM) of the system

If a particle moves in the $X-Y$ plane, the resultant angular momentum has

The moment of inertia of a uniform semi-circular disc of mass $M$ and radius $R$ about a line perpendicular to the plane of the disc through the centre is

Inertia is that property of a body by virtue of
which the body is

A flywheel is attached to an engine to

A particle is moving in a circular path. The correct statement out of the following is

Which one of the following has maximum inertia?

The moment of inertia of a disc of mass $\mathrm{M}$ and radius $\mathrm{R}$ about an axis which is tangent to the circumference of the disc and parallel to its diameter, is

If a force acts on a body at a point away from the centre of mass, then

A ring of mass $0.3 \mathrm{~kg}$ and radius $0.1 \mathrm{~m}$ and a solid cylinder of mass $0.4 \mathrm{~kg}$ and of the same radius are given the same KE and released simultaneously on a flat horizontal surface such that they begin to roll as soon as released towards a wall which is at the same distance from the ring and cylinder. Which will reach the wall first?

Position vector of centre of mass of two particles system is given by: