The efficiency of a machine is the ratio between ___

$\frac{V e l o c i t y r a t i o}{M e c h a n i c a l a d v a n t a g e}$

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$\frac{M e c h a n i c a l a d v a n t a g e}{V e l o c i t y r a t i o}$

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$\frac{M e c h a n i c a l a d v a n t a g e}{V e l o c i t y}$

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$\frac{M e c h a n i c a l a d v a n t a g e}{l o a d}$

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Solution

The correct option is B
$\frac{M e c h a n i c a l a d v a n t a g e}{V e l o c i t y r a t i o}$

Consider a machine which displaces an actual load W through a distance D, when effort E causes a displacement through distance d.
$∴$ Output of the machine
= Work done by the machine = W $\times$ D
$∴$ Input of the machine
= Work done on the machine = E $\times$ d
$∴$ Efficiency of the machine $(η)$ = $\frac{O u t p u t}{I n p u t}$
$= \frac{W \times D}{E \times d} = \frac{W}{E} \times \frac{D}{d}$
or $η = \frac{W}{E} \times \frac{D}{d}$ ...(i)
Now mechanical advantage (MA) of the system $= \frac{L o a d}{E f f o r t} = \frac{W}{E}$
Velocity ratio of the machine (VR)
$= \frac{D i s t a n c e m o v e d b y e f f o r t}{D i s t a n c e m o v e d b y l o a d} = \frac{d}{D}$
By substituting these two values of MA and VR in Eq.(i), we get:
$η = M A \times \frac{1}{V R} = \frac{M A}{V R}$
$∴$ Efficiency $= \frac{M e c h a n i c a l a d v a n t a g e}{V e l o c i t y r a t i o}$

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Similar questions

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

= 10

= 5

(a) State the relationship between mechanical advantage, velocity ratio and efficiency.

(b) Name the term that will not change for a machine of a given design.

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