Two blocks of masses 10   kg and 30   kg are placed on the same straight line with coordinates 0 ,…

Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates 0,0cm and x,0cm 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
  1. 4 cm towards the 10 kg block
  2. 2 cm away from the 10 kg block
  3. 2 cm towards the 10 kg block
  4. 4 cm away from the 10 kg block

Solution

Initial position of centre of mass: xCM=100+30×x40=3x4

Final position of the centre of mass: x'CM=106+30×x-y40=6+3x-y4

As position of centre of mass remains same,

xCM=x'CM ⇒3x4=6+3x-y4⇒3x=6+3x-3y  ⇒y=2 cm

Alternate method, ∆xCOM=m1∆x1+m2∆x2m1+m2⇒0=10×6+30y⇒y=-2 cm

Asked in: JEE Main 2022 (27 Jun Shift 1)

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