Can the mass of body be taken to be concentrated at its centre of mass for the purpose of calculating its rotational inertia?

A cricket bat is cut through its centre of mass into two parts as shown. Then, state whether both parts are of same mass or not. Also, give a reason.

Why in hand driven grinding machine, a handle is put near the circumference of the stone or wheel?

The bottom of a ship is made heavy. Why?

The moment of inertia of a disc about its diameter is \(\frac { { MR }^{ 2 } }{ 4 } \) , what will be its moment of inertia, an axis tangential to it and parallel to one of its diameter? [where M is mass of the disc and R is its radius.]

If earth contract to half its radius. What would be the length of the day?

What is the moment of inertia of a solid cylinder of mass M and radius R about axis tangential to cylinder surface and parallel to the axis of cylinder?

A fan of moment of inertia is 0.6 kg-m² is to be run upto a working speed of 0.5 rps. What is the angular momentum of the fan?

Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body ?

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? What is the linear acceleration of the rope ? Assume that there is no slipping.

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^-1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Give the location of the centre of mass of a Sphere.

Moment of inertia of a thin rod of length l about an axis passing through its one end and perpendicular to its length is MR²/3. Find the value of radius of gyration for the given scenario.

Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass Show \(K=K^{\prime}+1 / 2 M V^{2}\) where K is the total kinteic energy of the system of particles, K' is the total kinetic energy of the system when the particle velocities are taken with respect to the centre of mass and MV² /2 is the kinetic energy of the translation of the system as a whole (i.e., of the centre of mass motion of the system).The result has been used in Sec. 7.14

Two bodies of masses 1 kg and 2 kg are located at (1, 2) and (-1, 3), respectively. Calculate the coordinates of the centre of mass.

A comet revolves around the Sun in a highly elliptical orbit having a minimum distance of 7 x 10¹⁰ m and a maximum distance of 1.4 x 10¹³ m. If its speed while nearest to the sun is 60 kms^-1, Find its linear speed when situated from the sun.

Three masses 3 kg, 4 kg and 5 kg are located at the corners of an equilateral triangle of side lm, then what are the coordinates of centre of mass of this system.

A uniform disc of radius R and mass M is resting on table on its rim. The coefficient of friction between rim and table is \(\mu \). Now, disc is pulled with force F. What is the maximum value of F for which the disc rolls without slipping?

From a uniform disk of radius R, a circular hole of radius R/2 is cut out. The centre of the hole is at R/2 from the centre of the original disc. Locate the centre of gravity of the resulting flat body.