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: Balance idea
The centre of mass is the balance point. Each mass times its distance from that point must be equal on both sides.

Step 2: Equation
Let the point be $d$ from A. Then $2\times d = 4\times(9 - d)$.

Step 3: Solve
$2d = 36 - 4d$ gives $6d = 36$ and $d = 6$ cm.

Step 4: Check
The distance from B is $9 - 6 = 3$ cm, and $2 \times 6 = 12 = 4 \times 3$. The heavier particle B is closer to the balance point, as expected.

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