A uniform rod of mass m and length l suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, i $s _______.$ (g acceleration due to gravity)
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Question

A uniform rod of mass m and length l suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, i $s _______.$ (g acceleration due to gravity)

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G1 Physics · Accepted Answer

Immediately after one string is cut, the rod begins to rotate about the point of support of the remaining string. Taking torque about the supported end, mg × l ─── 2 = Iα. For a uniform rod about one end, I = ml² ──── 3 . Therefore, mg × l ─── 2 = ml² ──── 3 α. Hence, α = 3g ──── 2l . At that instant the centre of mass has tangential acceleration a₍CM₎ = α × l ─── 2 = 3g ─── 4 . Now apply vertical translation of the centre of mass: mg-T = m a₍CM₎. Therefore, mg-T = 3mg ──── 4 . Hence, T = mg-3m…

A uniform rod of mass m and length l suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, i s _______. (g acceleration due to gravity)