What is the fractional error in $g$ calculated from $T = 2\pi \sqrt {l/g} $ ? Given fraction errors in $T$ and $l$ are $ \pm x$ and $ \pm y$ respectively?

  • [AIIMS 2012]
  • A

    $x + y$

  • B

    $x -y$

  • C

    $2x + y$

  • D

    $2x -y$

Similar Questions

A student uses a simple pendulum of exactly $1 \mathrm{~m}$ length to determine $\mathrm{g}$, the acceleration due to gravity. He uses a stop watch with the least count of $1 \mathrm{sec}$ for this and records $40$ seconds for $20$ oscillations. For this observation, which of the following statement$(s)$ is (are) true?

$(A)$ Error $\Delta T$ in measuring $T$, the time period, is $0.05$ seconds

$(B)$ Error $\Delta \mathrm{T}$ in measuring $\mathrm{T}$, the time period, is $1$ second

$(C)$ Percentage error in the determination of $g$ is $5 \%$

$(D)$ Percentage error in the determination of $g$ is $2.5 \%$

  • [IIT 2010]

The percentage error in measurement of mass and speed are $3\%$ and $2\%$ then error in kinetic energy will be .......... $\%$

Two resistors ${R}_{1}=(4 \pm 0.8) \Omega$ and ${R}_{2}=(4 \pm 0.4)$ $\Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be

  • [JEE MAIN 2021]

Explain error of a sum or a difference.

A body travels uniformly a distance of $ (13.8 \pm 0.2)\,m$ in a time $(4.0 \pm 0.3)\, s$. The percentage error in velocity is  ......... $\%$