The diameter of a recessed ring measured by using two spherical balls of diameter $d_{1} = 60 m m$ and $d_{2} = 40 m m$ as shown in the figure

The distance $H_{1} = 35.55 m m$ and $H_{2} = 20.55 m m$ . The diameter (D, in mm) of the ring gauge is
93.3

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Solution

The correct option is A 93.3

$d_{1} = 60 m m, d_{2} = 40 m m$

$\frac{d_{1}}{2} = 30 m m; \frac{d_{2}}{2} = 20 m m$

$H_{1} = 35.55 m m, H_{2} = 20.55 m m$

$D = \frac{d_{1}}{2} + A B + \frac{d_{2}}{2}$

$B C = (H_{1} + \frac{d_{1}}{2}) - (H_{2} + \frac{d_{2}}{2})$

$= (35.55 + 30) - (20.55 + 20)$

$= (65.55) - (40.55) = 25 m m$

$In right angle Δ A B C$

$A C = \frac{d_{1}}{2} + \frac{d_{2}}{2} = 30 + 20 = 50 m m$

$A B = \sqrt{A C^{2} - 25^{2}} = 25 \sqrt{3} m m$

$D = 30 + 25 \sqrt{3} + 20 = 93.30 m m$

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