The pitch of a screw jack is 0.45cm and the arm is 60cm long. If the efficiency of the Jack is 75/π %, calculate the mechanical advantage.

1. Analyze the Question

We are given:

• Pitch ($p$): $0.45\text{ cm}$
• Length of arm ($R$): $60\text{ cm}$
• Efficiency ($\eta$): $\frac{75}{\pi}\%$
• Goal: Calculate the Mechanical Advantage (M.A.)

2. Explain the Concept

A screw jack is a simple machine. To solve this, we need two key formulas:

• Velocity Ratio (V.R.) of a screw jack: $V.R. = \frac{2\pi R}{p}$, where $R$ is the length of the arm and $p$ is the pitch.
• Efficiency ($\eta$): $\eta = \frac{M.A.}{V.R.} \times 100\%$. • Note: Since the efficiency is given as a fraction involving $\pi$, we will express the percentage as a decimal: $\eta = \frac{75}{\pi} \div 100 = \frac{75}{100\pi} = \frac{3}{4\pi}$.

3. Show the Solution

Step 1: Calculate the Velocity Ratio (V.R.)

To simplify, multiply the numerator and denominator by 100:

Step 2: Calculate the Mechanical Advantage (M.A.) Using the efficiency formula:

Now, solve for M.A.:

The $3$s cancel out, and the $\pi$s cancel out:

4. Identify the Answer

Comparing our result to the options provided: A. 400 B. 300 C. 200 D. 150

The calculated value matches option C.

5. Exam Tip

When dealing with circular motion in machines (like screw jacks or wheel and axles), always remember that the distance moved by the effort in one full rotation is the circumference of the circle described by the arm ($2\pi R$). If you see $\pi$ in the efficiency percentage, it is almost certainly there to cancel out the $\pi$ in your Velocity Ratio calculation—don't let it panic you!