A student performs an experiment for determination of g(=(4 π^2 l)/(T^2)), l 1 ~m , and he commits an error of Δ l . For T he takes the time of n oscillations with the stop watch of least count Δ T and he commits a

Correct answer: D. Δ L=0.1, Δ T=0.05, n=50 (Δ g)/(g)=(Δ l)/(l)+2 (Δ T)/(n) In option (d) error in Δ g is minimum and number of observations made are maximum. Hence, in this case error in g will be minimum.

JEE Advanced 2006

Exam: JEE Advanced
Year: 2006
Subject: Physics
Chapter: Mathematics in Physics

JEE Advanced 2006 · Physics · Mathematics in Physics

A student performs an experiment for determination of g(=(4 π^2...

A student performs an experiment for determination of

g\left(=\frac{4 \pi^2 l}{T^2}\right), l \approx 1 \mathrm{~m}

, and he commits an error of

\Delta l

. For

T

he takes the time of

n

oscillations with the stop watch of least count

\Delta T

and he commits a human error of

0.1 \mathrm{~s}

. For which of the following data, the measurement of

g

will be most accurate?

Options

A $\Delta L=0.5, \Delta T=0.1, n=20$
B $\Delta L=0.5, \Delta T=0.1, n=50$
C $\Delta L=0.5, \Delta T=0.01, n=20$
D $\Delta L=0.1, \Delta T=0.05, n=50$

Correct answer

D. $\Delta L=0.1, \Delta T=0.05, n=50$

Step-by-step solution

\frac{\Delta g}{g}=\frac{\Delta l}{l}+2 \frac{\Delta T}{n}

In option (d) error in

\Delta g

is minimum and number of observations made are maximum. Hence, in this case error in

g

will be minimum.

Practice Mathematics in Physics on Quantrex Academy →

More from Mathematics in Physics

The density ρ of a uniform cylinder is determined by measuring its mass m , length l and… JEE Main 2026 Four persons measure the length of a rod as 20.00 ~cm, 19.75 ~cm, 17.01 ~cm and 18.25 cm.… JEE Main 2026 In an experiment the values of two spring constants were measured as k_ 1 =(10 ± 0.2) N /… JEE Main 2026 Length, breadth and thickness of a strip having a uniform cross section are measured to… JEE Advanced 2025 A quantity Q is formulated as X^ -2 Y^ +(3)/(2) Z^ -(2)/(5) · X, Y and Z are independent… JEE Main 2025 A physical quantity C is related to four other quantities p, q, r and s as follows C=… JEE Main 2025 A physical quantity Q is related to four observables a, b, c, d as follows : Q= ab ^4 ~cd… JEE Main 2025 For an experimental expression y=(32.3 × 1125)/(27.4) , where all the digits are… JEE Main 2025 Full Mathematics in Physics list All JEE Advanced PYQs