The period of oscillating simple pendulum is T = 2π√(l/g) where… | MHT CET 2025 (22 Apr, Shift 1)

Q49MHT CET 2025 · 22 APR · SHIFT 1Medium

Errors in Measurement

The period of oscillating simple pendulum is $T = 2\pi\sqrt{\frac{l}{g}}$ where length ' $l$ ' is 100 cm with error 1 mm. Period is 2 second. The time of 100 oscillations is measured by a stopwatch of least count 0.1s. The percentage error in gravitational acceleration ' g ' is

Show answer and solution

Answer: (a)

$T = 2\pi\sqrt{l/g} \Rightarrow g = \frac{4\pi^2 l}{T^2}$ , so $\frac{\Delta g}{g} = \frac{\Delta l}{l} + 2\frac{\Delta T}{T}$ .
$\frac{\Delta l}{l} = \frac{0.1\text{ cm}}{100\text{ cm}} = 0.1\%$
Time for 100 oscillations $t = 200\text{ s}$ with $\Delta t = 0.1\text{ s}$ : $\frac{\Delta T}{T} = \frac{0.1}{200} = 0.05\%$
$\frac{\Delta g}{g} = 0.1\% + 2(0.05\%) = 0.2\%$
So the answer is (a) $0.2\%$ .

Report a mistake

More questions on Errors in Measurement

A physical quantity A can be determined by measuring parameters B, C, D and E using the…MHT CET 2025 (21 Apr, Shift 1)
The density of a cube is measured by measuring its mass and length of its sides. The \%…MHT CET 2025 (20 Apr, Shift 2)
The formula for the physical quantity is P = x³ yz² and the percentage error in the…MHT CET 2025 (19 Apr, Shift 1)
A quantity Q is formulated as X⁻² Y+3/2 Z-2/5. X, Y, and Z are independent parameters…JEE Main 2025 (8 Apr, Shift 2)
The energy of a system is given as E(t) = α³ e-β t, where t is the time and β = 0.3 s⁻¹…JEE Main 2025 (23 Jan, Shift 2)
A physical quantity C is related to four other quantities p, q, r and s as follows C =…JEE Main 2025 (3 Apr, Shift 2)
A physical quantity Q is related to four observables a, b, c, d as follows: Q = ab⁴cd…JEE Main 2025 (29 Jan, Shift 2)
In an electrical circuit, the voltage is measured as V = (200 ± 4) volt and the current…NEET 2024

Errors in Measurement question from MHT CET 2025 (22 Apr, Shift 1)

More questions on Errors in Measurement