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Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassMotion of centre of massMedium2 min

PhysicsMediumsingle choice

A plate in the form of a semicircle of radius R has a mass per unit area of kr where k is a constant and r is the distance from the centre of the straight edge. By dividing the plate into semicircular rings find the distance of the centre of mass of the plate from the centre of its straight edge.\\ (A) $\frac{4 R}{3 π}$ \\ (B) $\frac{2 R}{π}$ \\ (C) $\frac{3 R}{2 π}$ \\ (D) $\frac{3 R}{4 π}$

Options:

Answer:

Solution:

$dm = 2 π r k r dr = 2 πk r^{2} dr$ . Distance of CM of the differential ring from O: $r_{1} = \frac{2 r}{π}$ .

$r_{c m} = \frac{\int r _{1} dm}{\int dm} = \frac{\int _{0}^{R} 2 πk r ^{2} \frac{2 r}{π} dr}{\int _{0}^{R} 2 π r ^{2} k dr} = \frac{3 R}{4}$ .

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Motion of centre of mass

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