SATHEE: Rotation 3 Question 22

Rotation 3 Question 22

28. A solid cylinder rolls without slipping on an inclined plane inclined at an angle $θ$ . Find the linear acceleration of the cylinder. Mass of the cylinder is $M$ .

$(2005, 4$ M)

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Answer:

Correct Answer: 28. $\frac{2}{3} g \sin θ$ 29. $a_{C M} = \frac{4 F}{3 m_{1} + 8 m_{2}}, a_{plank} = \frac{8 F}{3 m_{1} + 8 m_{2}} = 2 a_{C M}$

(b) $\frac{3 F m_{1}}{3 m_{1} + 8 m_{2}}, \frac{F m_{1}}{3 m_{1} + 8 m_{2}}$

Solution:

For rolling without slipping, we have

$a = R α$

or $\frac{M g \sin θ - f}{M} = R \frac{f R}{\frac{1}{2} M R^{2}}$

$\begin{aligned} or & \frac{M g \sin θ - f}{M} & = \frac{2 f}{M} \\ ∴ & f & = \frac{M g \sin θ}{3} \end{aligned}$

Therefore, linear acceleration of cylinder,

$a = \frac{M g \sin θ - f}{M} = \frac{2}{3} g \sin θ$

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Rotation 3 Question 22

28. A solid cylinder rolls without slipping on an inclined plane inclined at an angle θ. Find the linear acceleration of the cylinder. Mass of the cylinder is M.

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28. A solid cylinder rolls without slipping on an inclined plane inclined at an angle $θ$ . Find the linear acceleration of the cylinder. Mass of the cylinder is $M$ .