# The length of a simple pendulum executing simple harmonic motion is increased by 21% The percentage increase in the time period of the pendulum of increased length is Option 1) 11% Option 2) 21% Option 3) 42% Option 4) 10%.

As we learnt in

Time period of oscillation of simple pendulum -

- wherein

l = length of pendulum

g = acceleration due to gravity.

Let the lengths of pendulum be $\dpi{100} (100l)$ and $\dpi{100} (121l)$

$\dpi{100} \therefore \; \; \; \; \frac{T'}{T}=\sqrt{\frac{121}{100}}=\frac{11}{10}$

$\dpi{100} \therefore \; \; \; \; Fractional \; change\; =\frac{T'-T}{T}=\frac{11-10}{10}=\frac{1}{10}$

$\dpi{100} \therefore \; \; \; \; Percentage \; change\; =10\, ^{0}/_{0}$

Correct option is 4.

Option 1)

11%

This is an incorrect option.

Option 2)

21%

This is an incorrect option.

Option 3)

42%

This is an incorrect option.

Option 4)

10%.

This is the correct option.

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