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%.

 

Answers (1)

As we learnt in

Time period of oscillation of simple pendulum -

T=2\pi \sqrt{\frac{l}{g}}

- wherein

l = length of pendulum 

g = acceleration due to gravity.

 

 

 

Let the lengths of pendulum be (100l) and (121l)

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

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

\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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