# If the load on a ball bearing is reduced to one third, then its life would increase by

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If the load on a ball bearing is reduced to one third, then its life would increase by
1. 3 times
2. 9 times
3. 27 times
4. 36 times
5. 81 times

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Correct Answer - Option 3 : 27 times

Concept:

The approximate rating of the service life of a ball or roller bearing is based on the given fundamental equation.

${\rm{L}} = {\left( {\frac{{\rm{C}}}{{\rm{P}}}} \right)^{\rm{k}}} \times {10^6}~{\rm{revolution}}$

where

L is rating lifeC is a basic dynamic loadP is the equivalent dynamic load

k = 3 for ball bearing

k = 10/3 for roller bearing

Calculation:

Given:

$L = {\left( {\frac{C}{P}} \right)^3}⇒ L \propto { {\frac{1}{P^3}} }\\ \therefore \;\frac{{{L_1}}}{{{L_2}}} ={\left( {\frac{P_2}{P_1}} \right)^3}= {{\frac {1}{3}}^3}\\ \therefore\; {L_1} = \frac{{{L_2}}}{{27}}$

⇒ L2 = 27 times L1