Error of Measurement

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Topic Question Set

Q 21 :

The time period of a simple harmonic oscillator is $T = 2 π \sqrt{\frac{k}{m}} .$ Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution.

Percentage error in determination of spring constant (k) is ______ %. [2026]

3.35
6.76
7.60
3.43

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(2)

Q 22 :

A spherical body of radius r and density $σ$ falls freely through a viscous liquid having density $ρ$ and viscosity $η$ and attains a terminal velocity $v_{0}$ . Estimated maximum error in the quantity $η$ is: (Ignore errors associated with $σ, ρ a n d g,$ gravitational acceleration) [2026]

$2 [[\frac{Δ r}{r} - \frac{Δ v_{0}}{v_{0}}]]$
$2 [[\frac{Δ r}{r} + \frac{Δ v_{0}}{v_{0}}]]$
$2 \frac{Δ r}{r} - \frac{Δ v_{0}}{v_{0}}$
$\frac{2 Δ r}{r} + \frac{Δ v_{0}}{v_{0}}$

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(4)

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