Question

A machine is operated by an effort of 25 N and the effort has a downward displacement of 2.5 m in raising a load of weight 100 N through 10 cm. What is the efficiency of machine (in %) ?

• A. 250
• B. 40
• C. 25
• D. 16

Answer 1

The correct option is D

16

The explanation for the correct answer

Step 1: Given Data

1. The effort$\left(E\right)$ that was given by the machine is$25N$.
2. The weight of the load$\left(L\right)$ is$100N$.
3. The displacement of the effort$\left(S_E\right)$ is$2.5m=\frac{25}{10}\times 100=250Cm$.
4. The displacement of the load$\left(S_L\right)$ is$10Cm$.

Step 2: Calculation of mechanical advantage

1. The mechanical advantage of a machine can be measured by calculating the ratio of the weight of the load to the effort given by the machine.
2. Mathematically,$mechanicaladvantage(MA)=\frac{Load\left(L\right)}{Effort\left(E\right)}$

$\Rightarrow MA=\frac{100}{25}=4$

Step 3: Calculation of velocity ratio

1. The velocity ratio can be calculated by calculating the ratio of displacement of effort to the displacement of load.
2. Mathematically,$velocityratio(V.R)=\frac{displacementofeffort\left(S_E\right)}{displacementofload\left(S_L\right)}$

$\Rightarrow V.R=\frac{250}{10}=25$

Step 4: Calculation of efficiency of the machine

1. The efficiency of the machine is measured as the ratio of the mechanical advantage of the machine to the velocity ratio.
2. Mathematically,$efficiency(in\%)=\frac{MA}{V.R}\times 100$

$\Rightarrow efficiency=\frac{4}{25}\times 100=16\%$

Hence, the efficiency of the machine is$16\%$.