Question

A machine part is shown in cross section in figure consists of two homogeneous solid, coaxial cylinders AB as the common axis. Where is its centre of mass from A? (in m)

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{52}{7}$
• D. $\frac{5}{7}$

Answer 1

The correct option is C $\frac{52}{7}$

As they are made us of same material

$\therefore \frac{M}{m}=\frac{V_{C_1}}{V_{C_2}}=\frac{2^2\times 12}{1^2\times 8}=6$

$\therefore M=6m$ ...(1)

$\therefore X_{CM}=\frac{M\times 6+m\times 16}{M+m}=\frac{6m\times 6+m\times 16}{7m}$

$=\frac{36+16}{7}=\frac{52}{7}$