Question

A bag contains 20 white balls and 4 red balls. One ball is drawn from the bag and it is replaced after noting its colour. In the second draw again one ball is drawn and its colour is noted and replaced. Find the probability of the event that both the balls are of different colours?

• A. 0.83
• B. 1.0
• C. 1.66
• D. 0.66

Hint:

Probability with replacement: Events are independent.
\(P(\text{different}) = P(W) \times P(R) + P(R) \times P(W)\).
Always check if replacement is specified.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Surface tension is the property of a liquid surface that causes it to contract and minimize its surface area. The excess pressure across a curved liquid surface depends on its radius and surface tension.

Step 2: Key Formula:
Using the relation adopted in this question, \[ \Delta P=\frac{2\sigma}{r} \] where \[ \Delta P=\text{pressure difference},\qquad \sigma=\text{surface tension},\qquad r=\text{radius}. \]

Step 3: Calculation:
Given: \[ \text{Diameter}=40\,\text{mm}=0.04\,\text{m} \] \[ r=0.02\,\text{m},\qquad \Delta P=2.5\,\text{N/m}^2 \] Substituting into the formula, \[ 2.5=\frac{2\sigma}{0.02} \] \[ \sigma=\frac{2.5\times0.02}{2} \] \[ \sigma=\frac{0.05}{2}=0.025\,\text{N/m} \]

Step 4: Final Answer:
\sigma=0.025 N/m} Hence, the correct option is (A).