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PhysicsSHMCalculation of time periodMedium2 minQB

PhysicsMediummultiple choice

A cylinder of mass $M$ and radius $R$ lies on a plank of mass $M$ as shown. The surface between plank and ground is smooth, and between cylinder and plank is rough. Assuming no slipping between cylinder and plank, and velocity amplitude of oscillation of plank to be V , mark the CORRECT alternative (s).

Options:(select one or more)

Answer:

A, B

Solution:

Using no slipping condition:

$a_{c} + α R = ap \frac{f}{M} + \frac{2 fR}{MR ^{2}} r = \frac{kx - f}{M}$

$\Rightarrow 4 f = kxkx - \frac{kx}{4} = Map \Rightarrow ap = (\frac{3 k}{4 M}) \times ω = \frac{3 k}{4 M}$

$T = 2 π \frac{4 M}{3 K} = 4 π \frac{M}{3 k} V = A \frac{3 k}{4 M} \Rightarrow A = \frac{4 M}{3 R} Vf = \frac{k}{4} \frac{4 M}{3 K} V = \frac{V}{2} \frac{Mk}{3}$

Stream:JEESubject:PhysicsTopic:SHMSubtopic:Calculation of time period

⏱ 2mℹ️ Source: QB

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