AP EAMCET · PHYSICS · Motion In Two Dimensions
A solid cylinder of mass \(m\) and radius \(\mathrm{R}\) rolls down an inclined plane of height \(\mathrm{h}\) without slipping. The speed of its centre of mass when it reaches the bottom is
- A \(\sqrt{(2 \mathrm{gh})}\)
- B \(\sqrt{\frac{4 \mathrm{gh}}{3}}\)
- C \(\sqrt{\frac{3 \mathrm{gh}}{4}}\)
- D \(\sqrt{\frac{4 \mathrm{~g}}{\mathrm{~h}}}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{\frac{4 \mathrm{gh}}{3}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { K. E. }=\frac{1}{2} \mathrm{I} \omega^2+\frac{1}{2} \mathrm{mv}^2 \\ & \text { K.E. }=\frac{1}{2}\left(\frac{1}{2} \mathrm{mr}^2\right) \omega^2+\frac{1}{2} \mathrm{mv}^2 \\ & =\frac{1}{4} \mathrm{mv}^2+\frac{1}{2} \mathrm{mv}^2=\frac{3}{4}…
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