If the length of the pendulum in pendulum clock increases

Question:

If the length of the pendulum in pendulum clock increases by $0.1 \%$, then the error in time per day is:

 

  1. $86.4 \mathrm{~s}$

  2. $4.32 \mathrm{~s}$

  3. $43.2 \mathrm{~s}$

  4. $8.64 \mathrm{~s}$


Correct Option: , 3

Solution:

$\mathrm{T}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}$

$\frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{1}{2} \frac{\Delta \ell}{\ell}$

$\Delta \mathrm{T}=\frac{1}{2} \times \frac{0.1}{100} \times 24 \times 3600$

$\Delta \mathrm{T}=43.2$

Ans. 3

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