MCQ
The length of simple pendulum is increased by $44\%$. The percentage increase in its time period will be ..... $\%$
- A$44$
- B$22$
- ✓$20$
- D$11$
✓
Answer
Correct option: C.
$20$
c
$\frac{\mathrm{T}_{1}}{\mathrm{T}_{2}}=\sqrt{\frac{\mathrm{L}_{1}}{\mathrm{L}_{2}}}$
$\frac{\mathrm{T}_{1}}{\mathrm{T}_{2}}=\sqrt{\frac{\mathrm{L}_{1}}{\mathrm{L}_{2}}}$
$\Rightarrow \frac{\mathrm{T}}{\mathrm{T}_{2}}=\sqrt{\frac{\mathrm{L}}{1.44 \mathrm{L}}}=\frac{10}{12}$
$\Rightarrow \mathrm{T}_{2}=1.2 \mathrm{T}$
$\Delta \mathrm{T}=0.2 \mathrm{T}$
$\Rightarrow \frac{\Delta \mathrm{T}}{\mathrm{T}} \times 100=20 \%$
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