Given:
Shaft Power, P = 7.46 kW = 7460 W
Speed, N = 1200 rpm
Shearing stress of shaft,
= 30 MPa
Shearing stress of key,
= 240 MPa
width of key, w = 
d is shaft diameter
Solution:
Torque, T = 
where,

= 59.365 N-m
Now,


d = 0.0216 m
Now,
w =
=
= 5.4 mm
Now, for shear stress in key
= 
we know that
T =
= F. 
⇒
= 
⇒
= 
length of the rectangular key, l = 4.078 mm
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The answer is "Conduct an experiment" :)
Vf^2 = vo^2 + 2ad
vf = 0 m/s
a = -9.8
0 = 10404 + 2 (9.8)d
10404 = 2 (9.8) d
d = 530.816
1528 - 530.816 = 997.184
Hope this helps