A machine with a velocity ratio of 6 is used to raise a load of 540\text{ N} by applying a… — JAMB UTME

A machine with a velocity ratio of $6$ is used to raise a load of $540\text{ N}$ by applying an effort of $120\text{ N}$ . What is the efficiency of the machine?

$75\%$ Answer
B
$133.3\%$
C
$22.2\%$
D
$450\%$

Answer

The efficiency of the machine is

75\%

The correct option is

75\%

. Mechanical Advantage is found by dividing the load (

540\text{ N}

) by the effort (

120\text{ N}

), giving

4.5

. Dividing this mechanical advantage by the given velocity ratio (

6

) and expressing as a percentage yields

\frac{4.5}{6} \times 100\% = 75\%

Step-by-Step Solution

Calculate Mechanical Advantage (MA)

\text{MA} = \frac{\text{Load}}{\text{Effort}} = \frac{540\text{ N}}{120\text{ N}} = 4.5

Mechanical advantage measures the force magnification produced by the machine.

Calculate Efficiency (\eta)

\eta = \left(\frac{\text{MA}}{\text{VR}}\right) \times 100\% = \left(\frac{4.5}{6}\right) \times 100\% = 75\%

Efficiency is the ratio of Mechanical Advantage to Velocity Ratio multiplied by 100%.

Key Concept

Efficiency of a Simple Machine

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