System of particles practice · Mixed difficulty

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

A solid sphere of mass 1 kg rolls down an inclined plane from rest from a height of 7m. On reaching the bottom rotational kinetic energy $K\left( {g = 10\,m{s^{ - 2}}} \right)$

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.

The radius of gyration of a disc of mass 50 g and radius 2.82 cm, about an axis passing through its centre of gravity and perpendicular to the plane, is

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

Moment of inertia of a uniform annular disc of internal radius $r$ and external radis $R$ and mass $M$ about an axis through its centre and perpendicular to its plane is

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

If the velocity of a rotating body of mass 50 kg is given by $\vec V = 3\vec i + 4\vec j + 5\vec k$ and rotating with radical vector $\overrightarrow r = 2\vec i + 3\vec j - 4\vec k$ , then its angular momentum is

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

Find the moment of inertia of a uniform square plate of mass $M$ and edge $a$ about one of its diagonals.

Two thin uniform circular rings each of radius 10 cm and mass 0.1 kg are arranged such that they have a common centre and their planes are perpendicular to each other. The moment of inertia of this system about an axis passing through their common centre and perpendicular to the plane of one of the rings in $kg\,{cm^2}$ is

A solid sphere of mass $m$ rolls down an inclined plane a height $h$. Find rotational kinetic energy of the sphere.

A stone is whirled along a circle with a constant angular velocity and its angular momentum is L. If the radius of its circular path is halved while keeping the angular velocity same, its new angular momentum would be

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

Three masses are placed on the x – axis, 200 g at origin, 400 g at x = 20 cm and 600 g at x = 60 cm. The distance of the centre of mass from the origin is

A spherical shell and a solid cylinder of same radius rolls down an inclined plane. The ratio of their accelerations 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

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 ?