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Q.

Find the centre of mass of right angular triangle sheet as shown in figure.

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a

$(\frac{a}{2}, \frac{b}{2})$

b

$(\frac{a}{5}, \frac{b}{5})$

c

$(\frac{a}{4}, \frac{b}{4})$

d

$(\frac{a}{3}, \frac{b}{3})$

answer is B.

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Detailed Solution

$\begin{array}{l} A = \frac{1}{2} a b, \frac{d m}{d a} = \frac{M}{A} \\ d m = \frac{M}{A} d a d A = y . d x, X_{c m} = \frac{1}{M} \int \frac{X (d A) M}{A} \\ \frac{1}{A} \int x (b - \frac{b}{a} x) . d x \\ X_{c m} = \frac{a}{3}, Y_{c m} = \frac{b}{3} \end{array}$

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