The center of mass of a hollow sphere of uniform density is located:

Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of centre of mass from first sphere is

The center of mass of a hollow sphere of uniform density is located:

The centre of mass of a body

Two spherical bodies of mass ‘M’ and ‘5M’ and radii ‘R’ and ‘2R’ released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

Two objects of mass 15 kg and 25 kg respectively are connected to the two ends of a rigid rod of length 12 m with negligible mass. The distance of the center of mass of the system from the 15 kg mass is:

If two particles of masses $3\,\,kg$ and $6\,\,kg$ which are at rest are separated by a distance of $15\,\,m.$. The two particles are moving towards each other under a mutual force of attraction. Then the ratio of distances travelled by the particles before collision is

Two particles of masses 2 kg and 3 kg are located at (1, 2) and (-1, 3) respectively. What are the coordinates of the center of mass of the system?

Which of the following statements are correct?

1. Centre of mass of body always coincides with the centre of gravity of the body.

2. Central mass of a body is the point at which the total gravitational torque on the body is zero.

3. A couple on a body produce both translational and rotational motion in a body.

4. Mechanical advantage greater than one means that small effort can be used to lift a large load.

A system consisting of two masses connected by a massless rod lies along the $x$- axis. A 0.4 kg mass is at a distance $x = 2m$, while a 0.6 kg mass is at a distance $x = 7m$. The $x$ co-ordinate of the centre of mass is

Two particles of equal mass are placed at a distance of L from each other. Where is their center of mass located?