Motion of Syste...

A solid cylinder of mass M and radius R rolls down an inclined plane without slipping. In doing so, it comes down a height h. The speed of its centre of mass when it reaches the bottom is

In a flywheel, mass is concentrated at the

Identify the correct statement(s) about the centre of mass.

Two bodies of mass 1 kg and 2 kg are located at (1, 2) and (- 1, 3) respectively. The co-ordinates of the centre of mass are

The moment of a couple is called

The angle turned by a body undergoing circular motion depends on time as θ = θ₀ + θ₁t + θ₂t². The angular acceleration of the body is

The moment of inertia of a body does not depend upon

The given shaped glass tube, having uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity 'ω', then

A shell at rest explodes. The centre of mass of the fragments

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

Three particles, each of mass 1 kg, are placed at the corners of a right-angled triangle AOB with O being the origin of the coordinate system (OA and OB along positive X-direction and positive Y-direction). If OA = OB = 1 m, then the positive vector of the centre of mass (in metres) is

The mass of moon is about 0.03 times that of Earth. The distance from the centre of moon to the centre of Earth is about 60 times the radius of Earth. How far is the centre of mass of system from the centre of Earth (R = 6400 km)?

A sphere is rolling on an inclined plane. What is the ratio of its rotational KE to the total KE?

A circular disc of radius R is removed from a bigger circular disc of radius 2R as shown in the figure. The centre of mass of the new disc is αR from the centre of the bigger disc. What is the value of α?

A thin circular ring of mass 'M' and radius 'r' is rotating about its axis with a constant angular velocity . Four objects, each of mass 'm', are kept gently on the opposite ends of two perpendicular diametres of the ring. The angular velocity of the ring will be

If a force 10 +  15 + 25 acts on a system and gives an acceleration 2 + 3 + 5 to the centre of mass of the system, the mass of the system is

Consider a system of two particles having masses m₁ and m₂. If the particle of mass m₁ is pushed toward the centre of mass of particles through a distance d, by what distance would the particle of mass m₂ move so as to keep the centre of mass of particles at the original position?

A cricket bat is cut at the location of its centre of mass as shown. Then,

Four identical spheres, each of mass 1 kg and radius 10 cm, are placed on a horizontal surface touching one another such that their centres are located at the corners of a square of side 20 cm. What is the distance of the centre of mass from the centre of sphere?

The angular velocity of a body changes from  to  without applying torque, but by changing moment of inertia. What is the ratio of the initial radius of gyration to the final radius of gyration?