Question

Balls of diameter 40 mm and 32 mm are used to measure the a angle of taper ring gage. The larger diameter ball is protruded by 8 mm above the end face of the gage and the distance from this face to the top of the smaller ball is 76 mm. The taper angle is

• A. ${11}^{\circ }{28}^{\prime }$
• B. $5^{\circ }{44}^{\prime }$
• C. ${22}^{\circ }{56}^{\prime }$
• D. $2^{\circ }{52}^{\prime }$

Answer 1

The correct option is B $5^{\circ }{44}^{\prime }$

$d_1=32$
$d_2=40$
$h_1=76$
$h_2=-8$

$\sin \frac{\theta }{2}=\frac{(d_2-d_1)}{2(h_1-h_2)-(d_2-d_1)}$

$=\frac{(40-32)}{2\left(84\right)-(40-32)}=\frac{8}{2\left(84\right)-8}$

$\sin \frac{\theta }{2}=0.05$

$\frac{\theta }{2}=2.86$

$\theta ={5.73}^{\circ }$

$\theta =5.73=5^{\circ }{44}^{\prime }$