Ncert Exercises & Solutions

Question 7. 16. From a uniform disk of radius R, a circular hole of radius R/2 is cut out. The centre of the hole is at R/2 from the centre of the original disc. Locate the centre of gravity of the resulting flat body.

Let

σ

is the mass per unit area.

Total mass,m =

σ π r^{2}

M a s s o f s m a l l e r d i s c = σ π {(\frac{r}{2})}^{2} = \frac{m}{4}

Centre of mass of the disc,

x_{c m} = \frac{m_{1} r_{1} + m_{2} r_{2}}{m_{1} + m_{2}}

= \frac{m \times 0 - \frac{m}{4} \times \frac{r}{2}}{m - \frac{m}{4}}

= - \frac{r}{6}

Hence the centre of mass is shifted

\frac{r}{6}

leftward from point O.

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