System of particles practice · Medium

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.

The moment of inertia $(I)$ and the angular momentum $(L)$ are related by the expression

Assertion: When a body dropped from a height explodes in mid air, its centre of mass keeps moving in vertically downward direction.
Reason: Explosion occur under internal forces only. External force is zero.

If the body is moving in a circle of radius r with a constant speed v, its angular velocity is

A 2 kg body and a 3 kg body are moving along the x-axis. At a particular instant the 2 kg body has a velocity of $3\;m{s^{ - 1}}$ and the 3 kg body has the velocity of $2m{s^{ - 1}}$. The velocity of the centre of mass at that instant is

A couple produces

2 bodies of different masses of 2 kg and 4 kg are moving with velocities 20 m/s and 10 m/s towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass

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

A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle $\theta$. The frictional force

Assertion: When you lean behind over the hind legs of the chair, the chair falls back after a certain angle.

Reason: Centre of mass lying outside the system makes the system unstable.

Assertion: A judo fighter in order to throw his opponent on to the mat tries to initially bend his opponent and then rotate him around his hip.
Reason: As the mass of the opponent is brought closer to the fighter's hip, the force required to throw the opponent is reduced.

Angular momentum is conserved

Three identical sphere lie at rest along a line on a smooth horizontal surface. The separation between any two adjacent spheres is L. The first sphere is moved with a velocity u towards the second sphere at time t=0. The coefficient of restitution for collision between any two blocks is 1/3. Then choose the correct statement

The centre of mass of a system of particles depends on

A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity. If the acceleration of lowest point on the disc $a$ and the velocity of the lowest point on the disc is $v$, then

A wheel of moment of inertia 10 kg ${m^2}$ is rotating at 10 rotations per minute. The work done in increasing its speed to 5 times its initial value, will be $\left( {{P^2}\,\, \approx \,\,10} \right)$

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

A solid cylinder (SC) a hollow cylinder (HC) and a solid sphere (S) of the same mass and radius are released simultaneously from the same height of incline. The order in which these bodies reach the bottom of the incline is

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

In which case application of angular velocity is useful

A cannon shell lands 2 km away from the cannon. A second shell, fired identically, breaks into two equal parts at the highest point. One part falls vertically. How far from the cannon will the other land ?

A body of mass 1 kg thrown with a velocity of $10\;\mathrm{m}{\mathrm{s}^{ - 1}}$ at an angle of ${60^0}$ with the horizontal. Its momentum at the highest point is

Two bodies of mass 10 kg and 2 kg are moving with velocities $\left( {2\hat i - 7\hat j + 3\hat k} \right)\,m/s$ and $\left( { - 10\hat i + 35\hat j - 3\hat k} \right)\,m/s$ respectively. The velocity of their centre of mass is

A particle of mass m moving with a velocity $\left( {3\hat i + 2\hat j} \right)m{s^{ - 1}}$ collides with a stationary body mass M and finally moves with a velocity $\left( { - 2\hat i + \hat j} \right)\mathrm{m}{\mathrm{s}^{ - 1}}.\,If\,\frac{m}{M} = \frac{1}{{13}},$ then

A tank filled with water is connected to another empty tank lying to the right side of the first tank. Until the level of water in the tanks become same
a) Centre of mass of water shifts down at constant rate
b) Centre of mass of water shifts down and rate of change of shift in centre of mass decreases gradually and becomes zero
c) Centre of mass shifts towards right as well

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

Two particles move towards each other from rest under a mutual force of attraction. At the instant, when the speed of A is V, the speed of B is V/2. The speed of centre of mass of the system is

A solid sphere rolls down two different inclined planes of same length, but of different inclinations. In both cases

Two points of a rod move with velocities 3v and v perpendicular to the rod and in the same direction separated by a distance 'r'. The angular velocity of the rod is

A flywheel of mass 50 kg and radius of gyration about its axis of rotation of 0.5m is acted upon by a constant torque of 12.5 Nm. Its angular velocity at t=5s is