Question

An offset is $15m$ long and the scale of plotting is $1cm=30m$ . If the accuracy in linear measurement is $1$ in $20$, permissible error in the angular measurement is

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. $0^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is C $0^{\circ }$

Displacement due to angular error on ground
$=l\sin \alpha =15\sin \alpha$
Displacement due to linear error on ground
$=\frac{l}{r}=\frac{15}{20}=0.75$
Combined error in plotting on plan = $=\frac{1}{30}\sqrt{(l\sin \alpha {)}^2+(0.75{)}^2}$
Hence
$\frac{1}{30}\sqrt{(15\sin \alpha {)}^2+(0.75{)}^2}=0.025$
$\Rightarrow \alpha =0^{\circ }$
Since $\alpha =0^{\circ }$
$\therefore$ No angular error can be permitted.