Question

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

Answer 1

Given:

The center of gravity of two cones of same height is found to differ by 2 cm.

To Find:

The height of the cones.

Solution:

• Center of gravity, from the base of a hollow cone is given by  Height/3.

• Center of gravity, from the base of a solid cone is given by  Height/4.

• So  center of gravity depends on height of the cone.

For two cones of same height, center of gravity can change in two ways :

1. The mass distribution is non uniform:

• This happens when base of the cone has more density than its upper part or vice versa.

     2. One of the cone is hollow and other is solid.

• In this we can apply the equation and find the height.

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

Therefore the height of the cones is 24 cm.