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STD 11 - 13. oscillations — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 13. oscillations4 Marks
MCQ
A simple pendulum is executing simple harmonic motion with a time period $T$. If the length of the pendulum is increased by $21\%$, the percentage increase in the time period of the pendulum of increased length is ..... $\%$
  • ✓
    $10$
  • B
    $21$
  • C
    $30$
  • D
    $50$
✓

Answer

Correct option: A.
$10$
a
(a) If initial length ${l_1} = 100$ then ${l_2} = 121$

By using $T = 2\pi \sqrt {\frac{l}{g}} $

$\Rightarrow \frac{{{T_1}}}{{{T_2}}} = \sqrt {\frac{{{l_1}}}{{{l_2}}}} $

Hence, $\frac{{{T_1}}}{{{T_2}}} = \sqrt {\frac{{100}}{{121}}} $

$\Rightarrow {T_2} = 1.1\,{T_1}$

$\%$ increase = $\frac{{{T_2} - {T_1}}}{{{T_1}}} \times 100 = 10\,\% $

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