A simple pendulum is released from A as shown in figure. If m and l represent mass of bob and length

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5.Work, Energy, Power and Collision

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A simple pendulum is released from $A$ as shown in figure. If $m$ and $l$ represent the mass of the $bob$ and the length of the pendulum respectively, the gain in kinetic energy at $B$ is

A

$\frac{{mgl}}{2}$

B

$\frac{{mgl}}{{\sqrt 2 }}$

C

$\frac{{\sqrt 3 }}{2}\,gml$

D

$\frac{2}{{\sqrt 3 }}\,gml$

Solution

Vertical height $=\mathrm{h}=\ell \cos 30^{\circ}$

Loss of potential energy $=\mathrm{mgh}$

$=\operatorname{mg} \ell \cos 30^{\circ}$

$=\frac{\sqrt{3}}{2} \mathrm{mg} \ell$

Kinetic energy gained $=\frac{\sqrt{3}}{2} \mathrm{mg} \ell$

Standard 11

Physics

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