To find the spring constant () of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of is

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Solution

Q.
To find the spring constant ( $k$ ) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of $k$ is: [2024]

1 3%

2 4%

3 5%

4 1%

Ans.
(1)

   $T = 2 π \sqrt{\frac{m}{k}} \Rightarrow k = 4 π^{2} \cdot \frac{m}{T^{2}}$

   $\frac{∆ k}{k} = \frac{∆ m}{m} + 2 \cdot \frac{∆ T}{T} \Rightarrow \frac{∆ k}{k} % = \frac{∆ m}{m} % + \frac{2 ∆ T}{T} %$

  (We always take maximum error)

   $\frac{∆ k}{k} % = (- 1) % + 2 (2) % = | - 3 % | = 3 %$

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