Question

If the units of power, work, and time are represented by \( x_1, x_2, x_3 \) respectively, then which of the following relations is correct?

• A. \( x_1 \times x_2 = x_3 \)
• B. \( x_1 \times x_3 = x_2 \)
• C. \( x_2 \times x_3 = x_1 \)
• D. \( x_1 \times x_2 \times x_3 = 1 \)

Hint:

Always remember the fundamental formula: \( P = \frac{W}{t} \). Rearranging this gives \( W = P \times t \), which is helpful for unit-based questions.

Answer 1

The Correct Option is B

Step 1: Recall the relation between power, work, and time.
Power is defined as work done per unit time: \[ P = \frac{W}{t} \] or, rearranging, \[ W = P \times t \] Step 2: Represent in given symbols.
If the units of power, work, and time are \( x_1, x_2, x_3 \) respectively, then: \[ x_2 = x_1 \times x_3 \] Step 3: Conclusion.
Hence, the correct relation is \( x_1 \times x_3 = x_2 \).