A rod OA of uniform mass density and length ‘L’ is hinged at O in a vertical plane. Another square plate of same mass is attached with a point A of the rod at its centre as shown in the figure. In case (i) square plate is free to rotate about point A and in case (ii) square plate is fixed at point A. Now, system is allowed to oscillate in vertical plane such that axis of rotation is horizontal and passing through point O. Let $$T1$$ and $$T2$$ are the time periods in case (i) and case (ii) respectively. If $$T1/T2$$ is $$m611$$. Find the value of m.

Question

A rod OA of uniform mass density and length ‘L’ is hinged at O in a vertical plane. Another square plate of same mass is attached with a point A of the rod  at its centre as shown in the figure. In case (i) square plate is free to rotate about point A and in case (ii) square plate is fixed at point A. Now, system is allowed to oscillate in vertical plane such that axis of rotation is horizontal and passing through point O. Let $$T1$$ and  $$T2$$ are the time periods in case (i) and case (ii) respectively. If $$T1/T2$$ is  $$m611$$. Find the value of m.

Infinity Learn · Accepted Answer

$$T1=2$$$$π$$$$l1mgd$$,$$l1=mL23+mL2T2=2$$$$π$$$$l1mgd$$,$$l2=mL23+mL/226+mL2$$ $$T1T2=l1l2=43611$$

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