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WBJEETwo solid cylinders \(P\) and \(Q\) of same mass and same radius start...
Two solid cylinders \(P\) and \(Q\) of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder \(P\) has most of its mass concentrated near its surface, while \(Q\) has most of its mass concentrated near the axis. Which statement(s) is(are) correct?
Solution:
As we know, acceleration of the center of mass of cylinder rolling down an inclined plane
\(a_{c}=\frac{g \sin \theta}{1+\frac{I}{M R^{2}}}\)
In case of \(P\) the mass is concentrated away from the axis, So \(I_{P}>I_{Q}\)
\(\therefore \quad a_{P} < a_{Q} \Rightarrow v_{\mathrm{P}} < v_{\mathrm{Q}} \Rightarrow \omega_{\mathrm{P}} < \omega_{\mathrm{Q}}\)
\(a_{c}=\frac{g \sin \theta}{1+\frac{I}{M R^{2}}}\)
In case of \(P\) the mass is concentrated away from the axis, So \(I_{P}>I_{Q}\)
\(\therefore \quad a_{P} < a_{Q} \Rightarrow v_{\mathrm{P}} < v_{\mathrm{Q}} \Rightarrow \omega_{\mathrm{P}} < \omega_{\mathrm{Q}}\)
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