JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Conservation of Momentum

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A rod of length 5L is bent right angle keeping one side length as 2L.

The position of the centre of mass of the system: (Consider L = 10 cm)

(A) $2 \hat{i} + 3 \hat{j}$
(B) $3 \hat{i} + 7 \hat{j}$
(C) $5 \hat{i} + 8 \hat{j}$
(D) $4 \hat{i} + 9 \hat{j}$ ✓ Correct

Answer: (D)

Solution

Take the bend at the origin, with the

2 L

arm along the

x

-axis and the

3 L

arm along the

y

-axis. The masses are proportional to the lengths,

2 m

and

3 m

, and each arm's centre lies at its midpoint: the horizontal arm at

(L, 0) = (10, 0)

cm and the vertical arm at

(0, 1.5 L) = (0, 15)

cm. The centre of mass is

x_{c m} = \frac{2 m ( 10 ) + 3 m ( 0 )}{5 m} = 4 cm, y_{c m} = \frac{2 m ( 0 ) + 3 m ( 15 )}{5 m} = 9 cm .

The centre of mass lies at

4 \hat{i} + 9 \hat{j}

cm.

JEE Main · 2025 · 07 Apr 2025 · Shift 1 · Single correct option

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