Two pendulums differ in lengths by $22\,cm$ . They oscillate at the same place such that one of them makes $15\,oscillations$ and the other makes $18\,oscillations$ during the same time. The lengths (in $cm$ ) of the pendulums are
Diffcult
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Total time is same for both pendulum
$\therefore \quad 15 \times(2 \pi \sqrt{\frac{\mathrm{x}}{\mathrm{g}}})=18(2 \pi \sqrt{\frac{\mathrm{x}-22}{\mathrm{g}}})$
$\Rightarrow 15 \times \sqrt{\mathrm{x}}=18 \sqrt{\mathrm{x}-22}$
$\Rightarrow \frac{x}{x-22}=\frac{36}{25} \Rightarrow x=72$ and $x-22=50$
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