The percentage error in measurement of a&nbsp | vedclass

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Question

$ m = k 	an 	heta$

$dm = k \sec ^{2} 	heta d 	heta$

$\Rightarrow \frac{ dm }{ m }=\frac{ k \sec ^{2} 	heta}{ k 	an 	heta} d 	heta$

$\

Vedclass · Accepted Answer

$45$

Vedclass · Answer

$ m = k 	an 	heta$

$dm = k \sec ^{2} 	heta d 	heta$

$\Rightarrow \frac{ dm }{ m }=\frac{ k \sec ^{2} 	heta}{ k 	an 	heta} d 	heta$

$\Rightarrow \frac{ dm }{ m }=\frac{ d 	heta}{\sin 	heta \cos 	heta}=\frac{2 d 	heta}{\sin 2 	heta}$

$\Rightarrow \%$ error is minimum when $\sin 2 	heta$ has maximum value

$2 	heta=\frac{\pi}{2}$ or $	heta=45^{\circ}$

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)

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