The time period of a simple pendulum is given by $T =2 \pi \sqrt{\frac{\ell}{ g }}$. The measured value of the length of pendulum is $10\, cm$ known to a $1\, mm$ accuracy. The time for $200$ oscillations of the pendulum is found to be $100$ second using a clock of $1s$ resolution. The percentage accuracy in the determination of $'g'$ using this pendulum is $'x'$. The value of $'x'$ to the nearest integer is ...........$\%$
The time period of a simple pendulum is given by $T =2 \pi \sqrt{\frac{\ell}{ g }}$. The measured value of the length of pendulum is $10\, cm$ known to a $1\, mm$ accuracy. The time for $200$ oscillations of the pendulum is found to be $100$ second using a clock of $1s$ resolution. The percentage accuracy in the determination of $'g'$ using this pendulum is $'x'$. The value of $'x'$ to the nearest integer is ...........$\%$
- [JEE MAIN 2021]
- A
$2$
- B
$3$
- C
$5$
- D
$4$
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- [AIEEE 2012]
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The International Avogadro Coordination project created the world's most perfect sphere using Silicon in its crystalline form. The diameter of the sphere is $9.4 \,cm$ with an uncertainty of $0.2 \,nm$. The atoms in the crystals are packed in cubes of side $a$. The side is measured with a relative error of $2 \times 10^{-9}$, and each cube has $8$ atoms in it. Then, the relative error in the mass of the sphere is closest to (assume molar mass of Silicon and Avogadro's number to be known precisely)
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- [KVPY 2021]