Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2014PhysicsMathematics in PhysicsActual

An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be :

Options

  1. A4.4%
  2. B2.27%
  3. C1.7%
  4. D2.7%

Correct answer

D. 2.7%

Step-by-step solution

T = 2 π L g ∴ T 2 = 4 π 2 L g ∴ g = 4 π 2 L T 2 % Error in g = Δ L L 0 × 1 0 0 + 2 Δ T T 0 × 1 0 0 = 1 × 1 0 - 3 0.20 × 1 0 0 + 2 1 9 0 × 1 0 0 = 0.5 + 2 1 0 9 = 0.5 + 2 0 9 = 0.5 + 2.22 = 2.7%

Practice Mathematics in Physics on Quantrex Academy →

More from Mathematics in Physics

The density of a uniform cylinder is determined by measuring its mass m , length l and diameter d . The measured values of m , l and d are 97.42 0.02 g, 8.35 0.05 mm and 20.20 0.02 2026Four persons measure the length of a rod as 20.00 ~cm , 19.75 ~cm , 17.01 ~cm and 18.25 cm. The relative error in the measurement of average length of the rod is : 2026In an experiment the values of two spring constants were measured as k₁=(10 0.2) N / m and k₂=(20 0.3) N / m . If these springs are connected in parallel, then the percentage error 2026Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm , 0.05 mm , and 6.0 ~m , respectively. Which of the following option(s) give(s) t 2025A quantity Q is formulated as X ⁻² Y ^ + 3 2 Z ^ - 2 5 X , Y and Z are independent parameters which have fractional errors of 0.1,0.2 and 0.5 , respectively in measurement. The max 2025A physical quantity C is related to four other quantities p , q , r and s as follows C = pq ^2 r ^3 ~s The percentage errors in the measurement of p , q , r and s are 1 %, 2 % 3 % 2025A physical quantity Q is related to four observables a, b, c, d as follows : Q = ab ^4 ~cd where, a =(60 3) Pa ; b =(20 0.1) m ; c =(40 0.2) Nsm ⁻² and d =(50 0.1) m , then the per 2025For an experimental expression y= 32.3 1125 27.4 , where all the digits are significant. Then to report the value of y we should write 2025 Full Mathematics in Physics list All JEE Main PYQs