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Q.

A homogeneous plate PQRST is as shown in figure. The centre of mass of plate lies at midpoint A of segment QT. Then the ratio of $\frac{b}{a} is (PQ = PT = b; QR = RS = ST = a)$

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a

$\sqrt{\frac{13}{2}}$

b

$\sqrt{\frac{13}{4}}$

c

$\frac{13}{2}$

d

$\frac{13}{4}$

answer is D.

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Detailed Solution

If centre of mass is at A

$a^{2} σ \frac{a}{2} = σ \frac{1}{2} absin θ \frac{1}{3} bsinθ$

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or $\frac{b}{a} = \sqrt{\frac{13}{4}}$

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A homogeneous plate PQRST is as shown in figure. The centre of mass of plate lies at midpoint A of segment QT. Then the ratio of ba is (PQ = PT = b; QR = RS = ST = a)