Center of MassHard
Question
Two men ′A′ and ′B′ are standing on a plank. ′B′ is at the middle of the plank and ′A′ is at the left end of the plank. Bottom surface of the plank is smooth. System is initially at rest and masses are as shown in figure. ′A′ and ′B′ start moving such that the position of ′B′ remains fixed with respect to ground and ′A′ meets ′B′. Then the point where A meets B is located at :
Options
A.the middle of the plank
B.30 cm from the left end of the plank
C.the right end of the plank
D.None of these
Solution
(C) Taking the origin at the centre of the plank.
m1ᐃx1 + m2 ᐃx2 + m3ᐃx3 = 0 (∵ ᐃxCM = 0)
(Assuming the centres of the two men are exactly at the axis shown.)
60(0) + 40(60) + 40 (−x) = 0 , x is the displacement of the block.
⇒ x = 60 cm i.e. A & B meet at the right end of the plank.
m1ᐃx1 + m2 ᐃx2 + m3ᐃx3 = 0 (∵ ᐃxCM = 0)
m1ᐃx1 + m2 ᐃx2 + m3ᐃx3 = 0 (∵ ᐃxCM = 0)
(Assuming the centres of the two men are exactly at the axis shown.)
60(0) + 40(60) + 40 (−x) = 0 , x is the displacement of the block.
⇒ x = 60 cm i.e. A & B meet at the right end of the plank.
m1ᐃx1 + m2 ᐃx2 + m3ᐃx3 = 0 (∵ ᐃxCM = 0)
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