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Center of Mass and Collision question

2012 · Q101
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Center of Mass and Collision question

2012 · Q101

NEETPhysicsCenter of Mass and CollisionMCQ+4 / −1
Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70cm. The distance of the centre of mass from the orgin is :
  1. A
    40 cm
  2. B
    45 cm
  3. C
    50 cm
  4. D
    30 cm
View written solutionFree

Correct answer: A

The distance of the centre of mass of the system of three masses from the origin O is

XCM=m1x1+m2x2+m3x3m1+m2+m3{X_{CM}} = {{{m_1}{x_1} + {m_2}{x_2} + {m_3}{x_3}} \over {{m_1} + {m_2} + {m_3}}}XCM​=m1​+m2​+m3​m1​x1​+m2​x2​+m3​x3​​

=300×0+500×40+400×70300+500+400 = {{300 \times 0 + 500 \times 40 + 400 \times 70} \over {300 + 500 + 400}}=300+500+400300×0+500×40+400×70​

=500×40+400×701200=400[50+70]1200 = {{500 \times 40 + 400 \times 70} \over {1200}} = {{400\left[ {50 + 70} \right]} \over {1200}}=1200500×40+400×70​=1200400[50+70]​

=50+703=1203=40 cm = {{50 + 70} \over 3} = {{120} \over 3} = 40\,cm=350+70​=3120​=40cm

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