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 $10 m$. If it dissipates $10 \%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is : [Use, $g: 10 ms^{-2}$ ]
(1) $6 \sqrt{5} ms^{-1}$
(2) $5 \sqrt{6} ms^{-1}$
(3) $5 \sqrt{5} ms^{-1}$
(4) $2 \sqrt{5} ms^{-1}$
Show Answer
Answer: (1)
Solution:
$\ell=10 m$
Initial energy $=mg \ell$
So, $\frac{9}{10} mg \ell=\frac{1}{2} mv^{2}$
$\Rightarrow \frac{9}{10} \times 10 \times 10=\frac{1}{2} v^{2}$
$v^{2}=180$
$v=\sqrt{180}=6 \sqrt{5} m / s$
