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Q.

The figure shows a metallic plate of uniform thickness and density. The value of l in terms of L so that the centre of mass of the system lies at the interface of the triangular and rectangular portion is

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a

$l = \frac{L}{2}$

b

$l = \frac{L}{3}$

c

$l = \frac{L}{\sqrt{3}}$

d

$l = \sqrt{\frac{2 L}{3}}$

answer is C.

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Detailed Solution

If the interface is taken as the origin then $\frac{l}{2} (bl) - \frac{L}{3} (\frac{1}{2} bL) = 0$

Center of mass of the triangle is $\frac{L}{3}$ from the base.

$(\frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}) = 0$

Here mass is proportional to area $I^{2} = \frac{L^{2}}{3}$

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The figure shows a metallic plate of uniform thickness and density. The value of l in terms of L so that the centre of mass of the system lies at the interface of the triangular and rectangular portion is