Ball Bearing

Consider a ball bearing is selected for a unique assembly. If the design requires a radial load of 0.7 N and a design life of 6, what is the minimum basic load rating?

Hint
The minimum required basic load rating (the load in which 90% of bearings from a given lot will survive 1 million revolutions) is:
$$$C=PL^{1/a}$$$
where $$C$$ is the minimum required basic load rating, $$P$$ is the design radial load, $$L$$ is the design life (in millions of revolutions), and $$a$$ is the bearing coefficient.
Hint 2
For ball bearings: $$a=3$$
For roller bearings: $$a=\frac{10}{3}$$
The minimum required basic load rating (the load in which 90% of bearings from a given lot will survive 1 million revolutions) is:
$$$C=PL^{1/a}$$$
where $$C$$ is the minimum required basic load rating, $$P$$ is the design radial load, $$L$$ is the design life (in millions of revolutions), and $$a$$ is the bearing coefficient. For roller bearings, $$a=10/3$$ . However, the problem statement is asking for a ball bearing, so $$a=3$$ . Thus,
$$$C=(0.7N)(6\cdot 10^6)^{1/3}=(0.7N)(181.71)=127.2\:N$$$
127.2 N