Work Power Energy Question 5
Question 5 - 2024 (29 Jan Shift 2)
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, $\mathrm{g}: 10 \mathrm{~ms}^{-2}$ ]
(1) $6 \sqrt{5} \mathrm{~ms}^{-1}$
(2) $5 \sqrt{6} \mathrm{~ms}^{-1}$
(3) $5 \sqrt{5} \mathrm{~ms}^{-1}$
(4) $2 \sqrt{5} \mathrm{~ms}^{-1}$
Show Answer
Answer: (1)
Solution:
$\ell=10 \mathrm{~m}$
Initial energy $=\mathrm{mg} \ell$
So, $\frac{9}{10} \mathrm{mg} \ell=\frac{1}{2} \mathrm{mv}^{2}$
$\Rightarrow \frac{9}{10} \times 10 \times 10=\frac{1}{2} \mathrm{v}^{2}$
$\mathrm{v}^{2}=180$
$\mathrm{v}=\sqrt{180}=6 \sqrt{5} \mathrm{~m} / \mathrm{s}$
