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Physics - Rotation Question with Solution | TestHub

PhysicsRotationTranslational + RotationalMedium2 minPYQ_2015

PhysicsMediumsingle choice

A uniform solid cylindrical roller of mass $m$ is being pulled on a horizontal surface with force $F$ parallel to the surface and applied at its centre. If the acceleration of the cylinder is $a$ and it is rolling without slipping then the value of $F$ is:

Options:

Answer:

Solution:

From free body diagram of cylinder

$F - f_{s} = m a$ .....(1)

$∵ \sum f_{e x t} = m a_{c m}$

$a l s o \sum τ_{e x t} = I_{c m} α$

$⟹ f_{s} R = I_{c m} α$

$⟹ f_{s} R = \frac{1}{2} m R^{2} α$ ..... (2)

For rolling without slipping

$a = R α$ ...... (3)

$⟹ α = \frac{a}{R}$

$∴ f_{s} R = \frac{1}{2} m R^{2} \frac{a}{R}$

$⟹ f_{s} = \frac{1}{2} m a$

Put in (1)

$F - \frac{1}{2} m a = m a$

$⟹ F = \frac{3}{2} m a$

Stream:JEESubject:PhysicsTopic:RotationSubtopic:Translational + Rotational

⏱ 2mℹ️ Source: PYQ_2015

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