The relationship between the mechanical advantage (MA), the velocity ratio (VR) and the efficiency (n) is:

M.A = $n \times V . R$

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V.R. = $n \times M . A$

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n= $M . A \times V . R$

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M.A = $n^{2} \times V . R$

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Solution

The correct option is A
M.A = $n \times V . R$

We know, Efficiency (n) = $\frac{W o r k o u t p u t}{W o r k i n p u t}$

Now, work output = Load (L) $\times$ displacement $(d_{L})$

Work input = Effort (E) $\times$ displacement $(d_{E})$

$\Rightarrow n = \frac{L \times d_{L}}{E \times d_{E}} = \frac{L}{E} \times \frac{1}{\frac{d_{E}}{d_{L}}}$
Also, we know $M . A . = \frac{L}{E} a n d V R = \frac{d_{E}}{d_{L}} \Rightarrow n = \frac{M . A}{V R} o r M A = n \times V . R$

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Similar questions

The correct relationship betwen the mechanical advantage (M.A.), the velocity ratio (V. R.) and the efficiency $η$ is :

(a) $M . A = η \times V . R .$ (b) $V . R = η \times M . A$

Derive a relationship between mechanical advantage, velocity ratio and efficiency of a machine.

(M . A .)

(V . R .)

(η)

(η)

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