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  • A square plate of edge d and a semicircular disc of radius d are arranged as shown in figure. The centre of the combination from centre of square plate is  <img alt="" src="https://c

A square plate of edge d and a semicircular disc of radius d are arranged as shown in figure. The centre of the combination from centre of square plate is 

Option: 1

\frac{9 \pi d-8 d}{6(2+\pi)}


Option: 2

\frac{8 \pi d -5d }{12\pi}


Option: 3

\frac{6 \pi d -8d }{8(2+\pi)}


Option: 4

\frac{3\pi d }{(1+\pi)}


Answers (1)

best_answer

As we have learned

Centre of Mass of semicircular plate -

It lies at a distance of \frac{4R}{3\pi} from centre of disc along the axis.

-

 

 x_{cm} = \frac{m_1\bar{x_1}+m_2\bar{x_2}}{m_1+m_2} \\\\ for\: \: plate \: \: x_1 = 0, \: \: m_1= \sigma (d^2) \\\\ for \: \: semicircular \: \: disc \\x_2 = \frac{d}{2} + \left ( d-\frac{4d}{3\pi} \right )\\\\ m_2 = \frac{1}{2} (\pi d^2)\sigma \\\\ x_{cm} = \frac{(\sigma d^2\times 0 )+ \frac{1}{2}\sigma (\pi d^2)[d/2 + (d-\frac{4d}{3 \pi})] }{\sigma d^2 + \frac{\sigma \pi d^2}{2} }

= \frac{9 \pi d -8d }{6(2+\pi)}

 

 

 

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chirag

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