JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Conservation of Momentum

Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates

(0, 0) cm

and (

x, 0

) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is :

(A)4 cm towards the 10 kg block
(B)2 cm away from the 10 kg block
(C)2 cm towards the 10 kg block✓ Correct
(D)4 cm away from the 10 kg block

Answer: (C)

Solution

For the center of mass to remain unchanged, the displacement of the center of mass must be zero:

Δ x_{G} = \frac{m _{1} Δ x _{1} + m _{2} Δ x _{2}}{m _{1} + m _{2}} = 0

Given

m_{1} = 10

kg moves

Δ x_{1} = + 6

cm (towards the 30 kg block), and

m_{2} = 30

kg:

0 = \frac{10 \times 6 + 30 \times Δ x _{2}}{40}

0 = 60 + 30Δ x_{2}

Δ x_{2} = - 2 cm

The negative sign indicates the 30 kg block moves 2 cm towards the 10 kg block.

Therefore, the answer is (C).

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Single correct option

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JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Conservation of Momentum

Solution

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