Question

If a 6 kg object moves 2 meter towards right then by what distance does 2 kg should move that centre of mass will remain at its initial position. ​​

Answer 1

Explanation:

here,

2 kg object have to move 6 meter towards left to remain the centre of mass at its initial position

explaination refer to attachment

Answer 2

The 2 kg object moves 6 meters towards left.

GIVEN

6 Kg object moves distance = 2 meter right

TO FIND

Distance travelled by 2 kg object so that the centre of mass will remain at its initial position.

SOLUTION

We can simply solve the above problem as follows;

Let, 6 kg object moves distance = Dx¹

2 kg object moved distance = Dx²

Change in Centre of mass = Dxᶜᵒᵐ

We know that,

Dxᶜᵒᵐ = 6Dx¹ + 2Dx²/ 6+2 (equation 1)

Since it is given that there is no change in centre of mass.

Dxᶜᵒᵐ = 0

Putting the value of Dxᶜᵒᵐ in equation 1

0 = 6×2 + 2Dx²/8

0 = 12 + Dx²

Dx² = 12/2 = -6 m (Minus sign denotes the object moves in opposite direction)

Hence , The 2 kg object moves 6 meters towards left.

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