A bob attached to a string is held horizontal | vedclass

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(A) Let the length of the string be $L$. When the bob is at a vertical distance $h$ below the point of suspension,the angle $	heta$ with the vertical

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(A) Let the length of the string be $L$. When the bob is at a vertical distance $h$ below the point of suspension,the angle $	heta$ with the vertical is given by $\cos 	heta = \frac{h}{L}$.Using the conservation of energy from the horizontal position (where $h=0$) to a position at depth $h$,the kinetic energy is $mgh = \frac{1}{2}mv^2$,so $v^2 = 2gh$.The forces acting on the bob are tension $T$ towards the center and the component of gravity $mg \cos 	heta$ away from the center. The net centripetal force is $T - mg \cos 	heta = \frac{mv^2}{L}$.Substituting $v^2 = 2gh$ and $\cos 	heta = \frac{h}{L}$:$T = \frac{m(2gh)}{L} + mg \left(\frac{h}{L}ight) = \frac{2mgh}{L} + \frac{mgh}{L} = \frac{3mgh}{L}$.Since $T = \left(\frac{3mg}{L}ight)h$,the relationship between $T$ and $h$ is linear,passing through the origin. This corresponds to the graph where $T$ increases linearly with $h$.

$A$ bob attached to a string is held horizontal and released. The tension $T$ and vertical distance $h$ from the point of suspension can be represented by which of the following graphs?

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