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(D) The maximum tension in the string of a simple pendulum occurs at the lowest point of its oscillation.At the lowest point,the tension $T$ is given

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$mg (1+	heta_0^2)$

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(D) The maximum tension in the string of a simple pendulum occurs at the lowest point of its oscillation.At the lowest point,the tension $T$ is given by $T = mg + \frac{mv^2}{l}$,where $v$ is the velocity at the lowest point.Using the principle of conservation of energy,the potential energy at the maximum angular displacement $	heta_0$ is converted into kinetic energy at the lowest point:$mgl(1 - \cos 	heta_0) = \frac{1}{2}mv^2$$v^2 = 2gl(1 - \cos 	heta_0)$Substituting $v^2$ into the tension equation:$T_{\max} = mg + \frac{m(2gl(1 - \cos 	heta_0))}{l}$$T_{\max} = mg + 2mg(1 - \cos 	heta_0)$For small angles,we use the approximation $\cos 	heta_0 \approx 1 - \frac{	heta_0^2}{2}$:$T_{\max} = mg + 2mg(1 - (1 - \frac{	heta_0^2}{2}))$$T_{\max} = mg + 2mg(\frac{	heta_0^2}{2})$$T_{\max} = mg(1 + 	heta_0^2)$

The angular amplitude of a simple pendulum is $\theta_0$. The maximum tension in its string will be

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