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JEE Main 20179 AprilOnline

Exam: JEE Main
Year: 2017
Date: 9 April
Mode: Online
Subject: Physics
Chapter: Oscillations

JEE Main 2017 · 9 April · Online · Physics · Oscillations

In an experiment to determine the period of a simple pendulum of...

In an experiment to determine the period of a simple pendulum of length

1m

, it is attached to different spherical bobs of radii

{r}_{1} and {r}_{2}

. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be

5 \times {10}^{- 4}s

, the difference in radii, \left|{r}_{1} - {r}_{2}\right| is best-given by

Options

A $0 . 01cm$
B $0 . 05cm$
C $0 . 5cm$
D $1cm$

Correct answer

B. $0 . 05cm$

Step-by-step solution

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

T ∝ \sqrt{l}

l = 1

\dfrac{\DeltaT}{T} = \dfrac{1}{2}\dfrac{\Deltal}{l}

\Deltal = {r}_{1} - {r}_{2}

⇒ ∆ l = \dfrac{2 ∆ T}{T} \times l

= \dfrac{2 \times 5 \times {10}^{- 4}}{2} \times 1m

= 5 \times {10}^{- 2}\text{cm}

= 0.05cm

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