Question

Two particles of masses \(2\) g and \(4\) g are situated at the opposite ends, A and B of a wooden bar respectively. Let \(l(AB) = 9\) cm. The center of mass of the system will be

• A. \(6\) cm from B.
• B. \(3\) cm from A.
• C. \(2\) cm from B.
• D. \(6\) cm from A.

Hint:

Place A at the origin and use the weighted average of positions.

Answer 1

The Correct Option is D

Step 1: Understand the concept
The centre of mass of two particles lies on the line joining them, closer to the heavier particle. Its position is the mass-weighted average of positions.

Step 2: Set up
Put A at \(x = 0\) with mass 2 g and B at \(x = 9\) cm with mass 4 g.

Step 3: Compute
\[ x_{cm} = \frac{2(0) + 4(9)}{2 + 4} = \frac{36}{6} = 6\ \text{cm} \]

Step 4: Interpret
The centre of mass is 6 cm from A, which is 3 cm from B. This is option (D). Options (A) and (B) swap which end is heavier, and (C) uses a wrong distance.

Final Answer:
The centre of mass is 6 cm from A. This is option (D). \[ \boxed{\text{(D) }6\ \text{cm from A}} \]