Question

The pitch of a spherometer is $1$ mm and there are $100$ divisions on its disc. It reads $3$ divisions on the circular scale above zero when it is placed on a plane glass plate. When it rests on a convex surface, it reads $2$ mm and $63$ divisions on a circular scale. If the distance between its outer legs is $4$ cm, the radius R of curvature of the convex surface is :

• A. $4cm$
• B. $2.6cm$
• C. $10.4cm$
• D. $6.3cm$

Answer 1

The correct option is C $10.4cm$

Pitch, $p$ $=$ $1mm$

Number of divisions N $=100$

Least count $C=\frac{p}{N}=0.01mm$

Zero error $=e=+nC=+3\left(0.01\right)=+0.03$mm

H $=2+nC=2+63\left(0.01\right)=2.63$ mm

Height of central leg above the feet of the outer legs $=h$
$h=H-e=2.63-0.03=2.60$ mm = $0.26cm$
$a=4cm$

Using spherometer formula R $=\frac{a^2}{6h}+\frac{h}{2}$

Substituting in spherometer formula

$=\frac{{\left(4\right)}^2}{6\left(0.26\right)}+\frac{0.26}{2}=10.4cm$