Half ring of mass m and radius R is released from the position shown in diagram. A small point mass of same mass is also fixed at the end as shown in figure. If the initial acceleration of point mass m is $\frac{2 g}{β π}$ then find the value of $β$ .

Question

CT43 n3 diagram

TestHub · Accepted Answer

For the half ring plus equal point mass, take moments about the hinge. The initial angular acceleration gives the endpoint tangential acceleration 2g/(3π). Comparing with 2g/(βπ) gives β=3.

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