Units And Measurement

Given the expression:

We are to find the dimensions of the constant using dimensional analysis.

Step 1: Determine dimensions of potential energy (V)

Gravitational potential has dimensions of energy per unit mass:

Step 2: Consider the second term

To ensure dimensional consistency with ,

However, the question implies that:

The expression must be dimensionally verified.

Step 3: Check dimensions of each quantity

• (electric charg\)

So,

If we interpret A as having dimensions of energy density per unit charge squared (in certain contexts), this can be valid under specific assumptions.

Hence, the correct match by dimensional comparison in the question’s context is:

Final Answer: Option (A):

The correct answer is option (A): 3

Significant figures refer to the digits that carry meaning contributing to the precision of a number. The rules to determine significant figures are:

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (zeros before the first non-zero digit) are not significant.
4. Trailing zeros (zeros after a decimal and a non-zero digit) are significant.
5. In scientific (exponential) notation, only the number before the exponent counts for significant figures.

Given number:

• Leading zeros "0.0" are not significant.
• Digits "6", "5", and the trailing zero "0" (after decimal) are significant.

So, the number of significant figures = 3

Answer: Option (A) — 3 significant figures