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Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassMotion of centre of massMedium2 min

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If the linear density of a rod of length 3m varies as $λ = 2 + x$ , then the position of centre of mass of the rod from origin is (given that rod is placed on positive x -axis, with one end at origin) :

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Answer:

Solution:

$x_{c m} = \frac{\int x d m}{\int d m} = \frac{\int _{0}^{L} ( 2 x + x ^{2} ) d x}{\int _{0}^{L} ( 2 + x ) d x} = \frac{\frac{2 L ^{2}}{2} + \frac{L ^{3}}{3}}{2 L + \frac{L ^{2}}{2}}$

Putting $L = 3 m$ ;

$x_{c m} = \frac{12}{7} m$

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

⏱ 2m

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