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Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassCalculate of COMMedium2 minQB

PhysicsMediumsingle choice

A square plate of variable mass density has mass '4m' and side length 'a'. It is kept as shown in figure. A point particle is kept on the plate. The y-coordinate of centre of mass of plate and particle system comes at same point if either a 'm' mass particle is kept at point A or a '4m' mass particle is kept at point B. Then y-coordinate of centre of mass of plate is :-

Options:

Answer:

Solution:

Let the plate's CM be at y. With m at A (height a): $y_{c m} = \frac{4 m y + ma}{5 m}$ . With 4m at B (height a/2): $y_{c m} = \frac{4 m y + 4 m ( a /2 )}{8 m}$ . Equating:

$8 (4 y + a) = 5 (4 y + 2 a) \Rightarrow 12 y = 2 a \Rightarrow y = \frac{a}{6}$

Ans. (A)

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Calculate of COM

⏱ 2mℹ️ Source: QB

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