Calculate the velocity ratio of a screw jack of pitch 0.2cm if the length of the tommy bar is 23cm

1. Analyze the question

We are asked to find the Velocity Ratio (V.R.) of a screw jack.

• Pitch ($p$): 0.2 cm
• Length of the tommy bar ($R$): 23 cm

2. Explain the concept

A screw jack is a simple machine. The velocity ratio of a screw jack is defined as the ratio of the distance moved by the effort (in one complete revolution) to the distance moved by the load (the pitch).

• In one complete revolution, the effort (applied at the end of the tommy bar) moves in a circle. The distance covered is the circumference of that circle: $2\pi R$.
• In that same revolution, the load moves forward by a distance equal to the pitch ($p$).

The formula is:

3. Show the solution

• Step 1: Identify the given values. • $R = 23 \text{ cm}$ • $p = 0.2 \text{ cm}$
• Step 2: Substitute the values into the formula. $$\text{V.R.} = \frac{2 \times \pi \times 23}{0.2}$$
• Step 3: Simplify the expression. $$\text{V.R.} = \frac{46\pi}{0.2}$$
• Step 4: Perform the division. To divide by 0.2, you can multiply both the numerator and denominator by 10: $$\text{V.R.} = \frac{460\pi}{2}$$ $$\text{V.R.} = 230\pi$$

4. Identify the answer

Comparing our result to the given options, the correct value is $230\pi$. This corresponds to option A.

5. Tip

When dealing with screw jacks, always remember that the "effort distance" is the circumference of the circle traced by the handle ($2\pi R$). If the question gives you the diameter of the tommy bar instead of the length (radius), remember to divide the diameter by 2 before using it in the formula!