Student Login

Home›Chapters›Units, Dimensions and Measurement PYQs›Errors in Measurement›Question 29

MHT CET 2026 (11 Apr, Shift 1) · Errors in Measurement

Errors in Measurement question from MHT CET 2026 (11 Apr, Shift 1)

Q29MHT CET 2026 · 11 APR · SHIFT 1Medium

Errors in Measurement

The period of oscillation of a simple pendulum is given by $T = 2\pi\sqrt{\frac{l}{g}}$ where $l$ is about $80$ cm and is known to have $0.1$ cm accuracy. The period is about $1.5$ s. The time of $50$ oscillations is measured by a stop watch of least count $0.1$ s. The percentage error in $g$ is nearly

Show answer and solution

Answer: (b)

$\frac{\Delta g}{g} = \frac{\Delta l}{l} + 2\frac{\Delta T}{T}$
$\frac{\Delta l}{l} = \frac{0.1}{80} = 0.125\%$
Time of 50 oscillations $= 50 \times 1.5 = 75\text{ s}$ , so $\frac{\Delta T}{T} = \frac{0.1}{75} = 0.133\%$
$\frac{\Delta g}{g} = 0.125\% + 0.267\% \approx 0.4\%$
So the answer is (b) $0.4$ .

Report a mistake

More questions on Errors in Measurement

The density ρ of a uniform cylinder is determined by measuring its mass m, length l and…JEE Main 2026 (6 Apr, Shift 1)
The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's…JEE Main 2026 (28 Jan, Shift 2)
A spherical body of radius r and density σ falls freely through a viscous liquid having…JEE Main 2026 (21 Jan, Shift 2)
In an experiment to determine the resistance of a given wire using Ohm's law, the…JEE Main 2026 (5 Apr, Shift 2)
The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The…JEE Main 2026 (2 Apr, Shift 1)
The time period of a simple harmonic oscillator is T = 2π√(m/k). Measured value of mass…JEE Main 2026 (28 Jan, Shift 2)
Which of the following comes under the category of random errors?MHT CET 2025 (23 Apr, Shift 1)
The initial and final temperatures of water as recorded by an observer are (38.6 ± 0.2)…MHT CET 2025 (19 Apr, Shift 2)