Two particles of masses 10kg and 30kg are lying on a straight line. The 10kg mass is shifted towards the 30kg mass by a distance of 2cm. By what distance should the 30kg mass be shifted so that the position of their centre of mass does not change

# Two particles of masses 10kg and 30kg are lying on a straight line. The 10kg mass is shifted towards the 30kg mass by a distance of 2cm. By what distance should the 30kg mass be shifted so that the position of their centre of mass does not change

1. A

2/3 cm towards 10kg

2. B

2/3 cm away from 10 kg

3. C

3/2 cm towards 10 kg

4. D

3/2 cm away from 10 kg

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### Solution:

$∆{\mathrm{X}}_{\mathrm{CM}}=0⇒\frac{{\mathrm{m}}_{1}∆{\mathrm{X}}_{1}+{\mathrm{m}}_{2}∆{\mathrm{X}}_{2}}{{\mathrm{m}}_{1}+{\mathrm{m}}_{2}}=0$

${\mathrm{m}}_{1}∆{\mathrm{X}}_{1}+{\mathrm{m}}_{2}∆{\mathrm{X}}_{2}=0$

$∆{\mathrm{X}}_{2}=\frac{-\mathrm{m}∆{\mathrm{X}}_{2}}{{\mathrm{m}}_{2}}=\frac{-2}{3}\mathrm{cm}$
2/3cm towards 10 kg

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