Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

If the length and time period of an oscillating pendulum have...

If the length and time period of an oscillating pendulum have errors of 11 % and 33 % respectively then the error in measurement of the acceleration due to gravity is

Options

  1. A44 %
  2. B55 %
  3. C66 %
  4. D77 %

Correct answer

D. 77 %

Step-by-step solution

Acceleration due to gravity ?
T=2πLgT2=4π2Lgg=4π2LT2Thus,∆gg×100=∆LL×100+2×∆TT×100=1+(2×3)T = 2\pi\sqrt{\dfrac{L}{g}}T^{2} = 4{π}^{2}\dfrac{L}{g}g = 4{π}^{2}\dfrac{L}{T2}Thus, \dfrac{∆ g}{g} \times 100 = \dfrac{∆ L}{L} \times 100 + 2 \times \dfrac{∆ T}{T} \times 100 = 1 + \left(2 \times 3\right) % = 1 + 6 = 7 %

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 2026Four persons measure the length of a rod as 20.00 ~cm, 19.75 ~cm, 17.01 ~cm and 18.25 cm.… JEE Main 2026In an experiment the values of two spring constants were measured as k_ 1 =(10 ± 0.2) N /… JEE Main 2026Length, breadth and thickness of a strip having a uniform cross section are measured to… JEE Advanced 2025A quantity Q is formulated as X^ -2 Y^ +(3)/(2) Z^ -(2)/(5) · X, Y and Z are independent… JEE Main 2025A physical quantity C is related to four other quantities p, q, r and s as follows C=… JEE Main 2025A physical quantity Q is related to four observables a, b, c, d as follows : Q= ab ^4 ~cd… JEE Main 2025For an experimental expression y=(32.3 × 1125)/(27.4) , where all the digits are… JEE Main 2025 Full Mathematics in Physics list All 99 Percentile Qs Bank for JEE Main PYQs