A solid sphere of mass m & radius R is cut into two equal parts and kept as shown. Find the height of centre of mass from the ground.

Engineering

Physics

Center of Mass

Calculus

Forces and Types of Forces

Question

A solid sphere of mass m & radius R is cut into two equal parts and kept as shown. Find the height of centre of mass from the ground.

$\frac{7 R}{8}$

$\frac{9 R}{8}$

$\frac{R}{2}$

$\frac{3 R}{8}$

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$y_{cm} = \frac{\frac{m}{2} \times \frac{3 R}{8} + \frac{m}{2} \times (\frac{3 R}{8} + R)}{m}$

$\frac{3 R}{16} + \frac{3 R}{16} + \frac{R}{2}$

$= \frac{3 R + 4 R}{8} = \frac{7 R}{8}$ .