Question

The percentage error in measurement of length and 'g' is 6% and 2% respectively. The percentage error in measurement of time period is?
a. 8%
b. 3%
c. 1.5%

Answer 1

Time period $\sf{T}$ depends upon length $\sf{l}$ and acceleration due to gravity $\sf{g}$ as,

$\longrightarrow\sf{T\propto\sqrt{\dfrac{l}{g}}}$

or,

$\longrightarrow\sf{T\propto l^{\frac{1}{2}}\,g^{-\frac{1}{2}}}$

Hence the percentage error in time period is given by,

$\longrightarrow\sf{\delta T=\dfrac{1}{2}\,\delta l+\dfrac{1}{2}\,\delta g}$

According to the question.

• $\sf{\delta l=6\%}$

• $\sf{\delta g=2\%}$

Hence,

$\longrightarrow\sf{\delta T=\dfrac{1}{2}\times6\%+\dfrac{1}{2}\times2\%}$

$\longrightarrow\sf{\delta T=3\%+1\%}$

$\longrightarrow\sf{\underline{\underline{\delta T=4\%}}}$