The period of oscillation of a… - JEE Main 2015 Physics PYQ

JEE Main 2015 — Physics Mechanics

2015mcqeasy

The period of oscillation of a simple pendulum is $T=2\pi \sqrt{\frac{l}{g}}.$ Measured value of $l$ is $20.0\mathrm{cm}$ , known to $1\mathrm{mm}$ accuracy and time for $100$ oscillations of the pendulum is found to be $90s$ using a wristwatch of $1s$ resolution. The accuracy in the determination of $g$ is

Official previous-year question

Held on 4 Apr 2015 · Verified 6 Jul 2026.

Options

A
$5%$
B
$4%$
C
$3%$
D
$1%$

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Solution

$\therefore T=2\pi \sqrt{\frac{l}{g}}\Rightarrow g=4{\pi }^{2}\frac{l}{{T}^{2}}$

$\therefore$ Error in $g$ can be calculated as

$\frac{\Delta g}{g}=\frac{\Delta l}{l}+\frac{2\Delta T}{T}$ .

$\therefore$ Total time for $n$ oscillation is $t=nT$ where $T$ = time for oscillation.

$\Rightarrow \frac{\Delta t}{t}=\frac{\Delta T}{T}$

$\Rightarrow \frac{\Delta g}{g}=\frac{\Delta l}{l}+\frac{2\Delta t}{t}$

Given that $\Delta l=1 \mathrm{mm}={10}^{-3} m, l=20\times {10}^{-2}m$

$\Delta t=1s, t=90s$ .

$% error in gis$

$\frac{\Delta g}{g}\times 100=(\frac{\Delta l}{l}+\frac{2\Delta t}{t})\times 100$

$=(\frac{{10}^{-3}}{20\times {10}^{-2}}+\frac{2\times 1}{90})\times 100$ $=\frac{1}{2}+\frac{20}{9}$ $=0.5+2.22$ $=2.72%$

$\cong 3%$

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Solution

$\therefore T=2\pi \sqrt{\frac{l}{g}}\Rightarrow g=4{\pi }^{2}\frac{l}{{T}^{2}}$

$\therefore$ Error in $g$ can be calculated as

$\frac{\Delta g}{g}=\frac{\Delta l}{l}+\frac{2\Delta T}{T}$ .

$\therefore$ Total time for $n$ oscillation is $t=nT$ where $T$ = time for oscillation.

$\Rightarrow \frac{\Delta t}{t}=\frac{\Delta T}{T}$

$\Rightarrow \frac{\Delta g}{g}=\frac{\Delta l}{l}+\frac{2\Delta t}{t}$

Given that $\Delta l=1 \mathrm{mm}={10}^{-3} m, l=20\times {10}^{-2}m$

$\Delta t=1s, t=90s$ .

$% error in gis$

$\frac{\Delta g}{g}\times 100=(\frac{\Delta l}{l}+\frac{2\Delta t}{t})\times 100$

$=(\frac{{10}^{-3}}{20\times {10}^{-2}}+\frac{2\times 1}{90})\times 100$ $=\frac{1}{2}+\frac{20}{9}$ $=0.5+2.22$ $=2.72%$

$\cong 3%$

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Solution

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JEE Main Mechanics in other years

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Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

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