A mass m is attached to a thin wire and whirl | vedclass

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(C) For a mass $m$ moving in a vertical circle of radius $R$,the tension $T$ in the wire at any angular position $	heta$ from the lowest point is giv

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the mass is at the lowest point

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(C) For a mass $m$ moving in a vertical circle of radius $R$,the tension $T$ in the wire at any angular position $	heta$ from the lowest point is given by the equation:$T - mg \cos 	heta = \frac{mv^2}{R}$$T = mg \cos 	heta + \frac{mv^2}{R}$At the lowest point,$	heta = 0^{\circ}$,so $\cos 0^{\circ} = 1$. Also,the velocity $v$ is maximum at the lowest point due to the conservation of energy.Since both $\cos 	heta$ and $v$ are at their maximum values at the lowest point,the tension $T$ is maximum at this position.Therefore,the wire is most likely to break when the mass is at the lowest point.

List-$I$ (Speed at lowest point)	List-$II$ (Possible situation)
$(P) v_0 = \sqrt{5 g \ell}$	$(1)$ Tension at lowest point $= 6 mg$
$(Q) v_0 = \sqrt{g \ell}$	$(2)$ String will slack for a finite time
$(R) v_0 = 2 \sqrt{g \ell}$	$(3)$ Bob will oscillate
$(S) v_0 = 3 \sqrt{g \ell}$	$(4)$ Tension at highest point $= 4 mg$

$A$ mass $m$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when

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