Question 66: Oscillations

Question

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $$10 \mathrm{~m}$$. If it dissipates $$10 \%$$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is:
[Use, $$\mathrm{g}: 10 \mathrm{~ms}^{-2}$$]

Accepted Answer

$$\ell=10 \mathrm{~m}$$,
Initial energy $$=\mathrm{mg} \ell$$
$$\begin{aligned}
& 	ext { So, } \frac{9}{10} \mathrm{mg} \ell=\frac{1}{2} \mathrm{mv}^2 \
& \Rightarrow \frac{9}{10} 	imes 10 	imes 10=\frac{1}{2} \mathrm{v}^2 \
& \mathrm{v}^2=180 \
& \mathrm{v}=\sqrt{180}=6 \sqrt{5} \mathrm{~m} / \mathrm{s}
\end{aligned}$$

Answer

$$5 \sqrt{6} \mathrm{~ms}^{-1}$$

Answer

$$5 \sqrt{5} \mathrm{~ms}^{-1}$$

Answer

$$2 \sqrt{5} \mathrm{~ms}^{-1}$$

Answer

$$6 \sqrt{5} \mathrm{~ms}^{-1}$$

Oscillations

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10 \mathrm{~m}. If it dissipates 10 \% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, \mathrm{g}: 10 \mathrm{~ms}^{-2}$]

Choose the correct answer: