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QJEEM22Ph543d: JEE Main 2022 Physics - Class 11 JEEM22Ph543d Solution: In an experiment to find acceleration due to gravity (g) using…

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s0.5 \mathrm{~s} is measured from time of 100 oscillation with a watch of 1 s1 \mathrm{~s} resolution. If measured value of length is 10 cm10 \mathrm{~cm} known to 1 mm1 \mathrm{~mm} accuracy, The accuracy in the determination of g\mathrm{g} is found to be x%x \% . The value of xx is ___________.

Step-by-Step Verified Solution

T=2πlgT = 2\pi \sqrt {{l \over g}}

dgg×100=2dTT×100+dll×100{{dg} \over g} \times 100 = {{2dT} \over T} \times 100 + {{dl} \over l} \times 100

=2×150×100+1100×100=5%= 2 \times {1 \over {50}} \times 100 + {1 \over {100}} \times 100 = 5\%

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