A stick has its bottom end attached to a wall | vedclass

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(C) Let $L$ be the length of the stick and $m$ be its mass. The weight $mg$ acts at the center of mass,which is at a distance $L/2$ from the pivot.Tak

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(C) Let $L$ be the length of the stick and $m$ be its mass. The weight $mg$ acts at the center of mass,which is at a distance $L/2$ from the pivot.Taking torque about the pivot point:$	au_{	ext{pivot}} = 0$$mg \left( \frac{L}{2} \sin 	heta ight) = T \cdot L \sin \phi$where $\phi$ is the angle between the stick and the string.$T = \frac{mg \sin 	heta}{2 \sin \phi}$To minimize $T$,we need to maximize $\sin \phi$. The maximum value of $\sin \phi$ is $1$,which occurs when $\phi = 90^\circ$.In scenario $B$,the string is horizontal and the stick makes an angle $	heta$ with the wall,so the angle between the stick and the string is $\phi = 90^\circ - 	heta$. This is not necessarily $90^\circ$.In scenario $C$,the string is perpendicular to the stick,so $\phi = 90^\circ$. This gives the minimum tension $T = \frac{mg \sin 	heta}{2}$.

$A$ stick has its bottom end attached to a wall by a pivot and is held up by a massless string attached to its other end. Which of the following scenarios has the smallest tension in the string? (Length of stick is same in all scenarios)

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