Question

in the expression for time period T = 2π√l/g if percentage error in measurement of time period & length are 2%& 2% respectively then percentage error in acceleration due to gravity is??​

Answer 1

Solution:

Given:

=> Error percentage of time period = 2%.

=> Error percentage of length = 2%.

To find:

=> Error percentage in acceleration due to gravity.

So,

$\sf{\implies \dfrac{\Delta T}{T}=2\% = \dfrac{2}{100}=0.02}$

$\sf{\implies \dfrac{\Delta L}{L}=2\% = \dfrac{2}{100}=0.02}$

Given Equation,

$\sf{\implies T = 2\pi \sqrt{\dfrac{L}{g}}}$

=> g = 4π²L/T²

=> Δg/g = 2ΔL/L + 2ΔT/T

=> Δg/g = 2 × 0.02 + 2 × 0.02

=> Δg/g = 0.04 + 0.04

=>  Δg/g = 0.08

Thus, (Δg/g)% = 0.08×100 = 8%

So, percentage error in acceleration due to gravity is 8%.

Answer 2

Answer:

the answer is 6%.

Explanation:

refer to the above attachment.

thanks for asking.

hope it helps.