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1.Units, Dimensions and Measurement
hard
The percentage error in measurement of a physical quantity $m$ given by $m = \pi \tan \theta $ is minimum when $\theta $ $=$ .......... $^o$ (Assume that error in $\theta $ remain constant)
A
$45$
B
$90$
C
$60$
D
$30$
Solution
$ m = k \tan \theta$
$dm = k \sec ^{2} \theta d \theta$
$\Rightarrow \frac{ dm }{ m }=\frac{ k \sec ^{2} \theta}{ k \tan \theta} d \theta$
$\Rightarrow \frac{ dm }{ m }=\frac{ d \theta}{\sin \theta \cos \theta}=\frac{2 d \theta}{\sin 2 \theta}$
$\Rightarrow \%$ error is minimum when $\sin 2 \theta$ has maximum value
$2 \theta=\frac{\pi}{2}$ or $\theta=45^{\circ}$
Standard 11
Physics
