A pendulum has length of $0.4 \mathrm{~m}$ and maximum speed $4 \mathrm{~m} / \mathrm{s}$. When the length makes an angle $30^{\circ}$ with the horizontal, its speed will be $\left[\sin \frac{\pi}{6}=\cos \frac{\pi}{3}=0 \cdot 5\right.$ and $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$

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Aicharya · Accepted Answer

A pendulum has length of $0.4 \mathrm{~m}$ and maximum speed $4 \mathrm{~m} / \mathrm{s}$. When the length makes an angle $30^{\circ}$ with the horizontal, its speed will be $2 \sqrt{3} \mathrm{~m} / \mathrm{s}$. Explanation: $h=L-L \cos 0=L(1-\cos 	heta)$ $=0.4\left(1-\cos 60^{\circ}ight)$ $=0.4\left(1-\frac{1}{2}ight)$ $=0.4 	imes \frac{1}{2}$ $=0.2$ $\frac{1}{2} m v_{1}^{2}=\frac{1}{2} m v_{2}^{2}+m g h$ $v_{1}^{2}=v_{2}^{2}+2 g h$ $	herefore v_{2}^{2}=v_{1}^{2}-2 g h$ $=(4)^{2}-2 	imes 10 	imes 0.2$ $=16-4=12$ $	herefore v_{2}=\sqrt{12}=2 \sqrt{3} m / s$

A pendulum has length of $0.4 \mathrm{~m}$ and maximum speed $4 \mathrm{~m} / \mathrm{s}$. When the length…

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