Question

The centre of gravity of two cones of same height is found to differ by 2 cm. when is it possible? find the height of the cones

Answer 1

The center of gravity of two cones of same height is found to differ by 2 cm. It is it possible when the density ( mass distribution) is not uniform in either of the cones.

Height of the cones is 24cm.

While deriving the expression for center of mass of a cone,

• we assume that the mass is evenly distributed across its volume for a solid sphere and across its area for a hollow sphere.

• If the distribution is not even, the lower part may be heavier than the upper part or upper part may be heavier than the lower part.
• This could shift the position of center of mass either down or up.
• In  this scenario, its possible that one of the cone may have a uniform distribution while other have non uniform distribution.

In other case ,

• one cone can be Hollow and other solid.
• Let H be the height of the cones.
• For Hollow sphere Center of mass = H/3 from the bottom.
• For Solid Shpere , Center of mass = H/4 from the bottom.

so Height difference  = 2cm = >

• H/3 - H/4 = 2cm
• H/12 = 2cm
• H = 24cm.