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The maximum efficiency of a machine 
1. is directly proportional to the velocity ratio  
2. should occur when the load is 50% of maximum permissible load 
3. is given by mechanical advantage divided by velocity ratio 
4. is given by velocity ratio divided by mechanical advantage

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Correct Answer - Option 3 : is given by mechanical advantage divided by velocity ratio 

Explanation:

Efficiency:

It is the ratio of output to input. In a simple mechanism, it is also defined as the ratio of mechanical advantage to the velocity ratio.

\(\eta = \frac{{Output}}{{Input}} = \frac{{M.A}}{{V.R}}\)

In an ideal machine, the mechanical advantage is equal to the velocity ratio.

Mechanical Advantage (MA):

In a simple machine when the effort (P) balances a load (W), the ratio of the load to the effort is called Mechanical Advantage.

\(M.A = \frac{{Load}}{{Effort}} = \frac{W}{P}\)

Velocity Ratio:

It is the ratio between the distance moved by the effort to the distance moved by the load.

\(V.R = \frac{{Distance\;moved\;by\;the\;effort\;\left( {{d_P}} \right)}}{{Distance\;moved\;by\;the\;load\;\left( {{d_w}} \right)}}\)

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