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In the arrangements as shown, mass of block $A i s m .$ What should be the mass of the block $B$ so that magnitude of acceleration of centre of mass of both the blocks is zero ?

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$\frac{m}{2}$

$\frac{m \sqrt{3}}{2}$

$m \sqrt{2}$

$\frac{m}{\sqrt{3}}$

answer is D.

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Detailed Solution

${\vec{a}}_{c o m} = \frac{M \vec{a_{1}} + m \vec{a_{2}}}{(m + M)},$ But $| \vec{a_{1}} | = | \vec{a_{2}} |$

Accelerating of system= $\frac{M g \sin 60^{0} - m g \sin 30^{0}}{(m + M)} = \frac{M \vec{a_{1}} + m \vec{a_{2}}}{(m + M)} = 0, M \neq 0, m \neq 0$

It is possible if $| \vec{a_{1}} | = | \vec{a_{2}} | = 0$ Or $M g \sin 60^{0} = m g \sin 30^{0}, M = \frac{m}{\sqrt{3}}$

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