System of particles practice · Medium

Assertion: A person standing on a rotating platform suddenly stretched his arms, the platform slows down.
Reason: A person by stretching his arms increases the moment of inertia and decreases angular velocity.

Assertion: Toppling is the application of the centre of mass.
Reason: Toppling stability determines the maximum angle that an object can be tilted before it will topple over.

A body of mass $1.5 \mathrm{~kg}$ rotating about an axis with angular velocity of $0.3 \mathrm{rad} \mathrm{s}^{-1}$ has the angular momentum of $1.8 \mathrm{~kg}$ $\mathrm{m}^2 \mathrm{~s}^{-1}$. The radius of gyration of the body about an axis is

The moment of inertia of a straight thin rod of mass M and length L about an axis perpendicular to its length and passing through one end is

A fan is rotating with an angular speed 300 rpm. The fan is switched off, and it takes $80 \mathrm{~s}$ to come to rest. Assuming constant angular deceleration, the number of revolutions made by the fan before it comes to rest is

Calculate the angular momentum of a body whose rotational energy is 10 Joule. If the angular momentum vector coincides with the axis of rotation and its moment of inertia about this axis is $8 \times {10^{ - 7}}\;kg\;{m^2}$

If a solid sphere, disc and cylinder are allowed to roll down an inclined plane from the same height

A circular turn table has a block of ice placed at its centre. The system rotates with an angular speed $\omega$ about an axis passing through the centre of the table. If the ice melts on its own without any evaporation, the speed of rotation of the system

A mass of 10 kg connected at the end of a rod of negligible mass is rotating in a circle of radius 30 cm with an angular velocity of $10\;rad/sec$. If this mass is brought to rest in 10 sec by a brake, what is the magnitude of the torque applied

Assertion: The angular momentum of a body is equal to twice the product of its mass and areal velocity.
Reason: When no external torque acts, the motion of the body takes place in a fixed plane.

From an inclined plane a sphere, a disc, a ring and a spherical shell are rolled without slipping. The order of their reaching at the base will be

If the origin of co-ordinate system lies at the centre of mass, the sum of the moments of the masses of the system about the centre of mass

In rotational motion of a rigid body about an axis, particles move with:

If the earth is treated as a sphere of radius R and mass M; its angular momentum about axis of rotation with period T is

Identify the correct statement. In the absence of external force,
a) the kinetic energy associated with the motion of centre of mass is conserved
b) Centre of mass is not accelerated
c) The centre of mass always move in curved line
d) Centre of mass must be at rest

A flywheel having moment of inertia $10 \mathrm{~kg} . \mathrm{m}^2$ is rotating at $50 \mathrm{~rad.s}^{-1}$. What amount of work needs to be done in order to bring this flywheel to rest in 10 seconds?

In free space, a shell moving with velocity $60\,m/s$ along the positive x-axis. When it passes through origin, it explodes into two pieces of mass ratio 1: 2. After the explosion, the velocity of the centre of mass is:-

A particle with position vector $r$ has a linear momentum $p$. Which of the following statements is true in respect of its angular momentum L about the origin

A rigid body of mass $m$ rotates about an axis passing through its centre. If the angular velocity of the body is unity, the moment of inertia of the body will be equal to

A ball kept in a closed box moves in the box making collisions with the walls. The box is kept
on a smooth surface. The center of mass

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

Statement-I: A coin is placed on phonogram turn table. The motor is started, coin moves along the moving table.
Statement-II: The rotating table is providing necessary centripetal force to the coin.

Assertion: As star collapse its angular velocity increases.
Reason: The mass of star decreases.

An astronaut is rotated in a horizontal circle at a radius of $5 \mathrm{~m}$. If the astronaut can withstand a maximum acceleration of $7 \mathrm{~g}$, then maximum numbers of permissible revolution per second is $\left(1 \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2\right)$.

When an external force is applied at the centre of mass of a rigid body at rest, then it undergoes

Assertion: Location of centre of mass is independent of the reference frame.
Reason: Centre of mass is same as centre of gravity.

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass ‘m’ is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period

A solid cylinder of radius $4 \mathrm{~cm}$ and mass $250 \mathrm{~g}$ rolls down an inclined plane (1 in 10). Calculate the acceleration and the total energy of the cylinder after $5 \mathrm{~s}$.

The radius of gyration of disc of mass and radius $R$ about an axis which is at distance $2 R$ from its centre and in the plane of the disc will be

A particle of mass 1 kg is projected with an initial velocity 10 $\mathrm{m}{\mathrm{s}^{ - 1}}$  at an angle of projection ${45^0}$ with the horizontal. The average torque acting on the projectile, between the time at which it is projected and the time at which it strikes the ground, about the point of projection in newton-metre is