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Question

Two balls A and B of equal masses are projected upward simultaneously, one from the ground with speed 50 ms1 and other from height 40 m above the first ball high tower with initial speed 30 ms1. Find the maximum height attained by their centre of mass.

  1. 20 m
  2. 100 m
  3. 80 m
  4. 60 m


Solution

The correct option is B 100 m
The initial position of centre of mass is
ycm=m×0+m×402m=20m
Initial velocity of centre of mass ucm=m×50+m×302m=40ms1
Acceleration of centre of mass, acm=g
Using kinematics equation: v2cm=u2cm+2acmH
Here H is the maximum height reach by centre of mass of two balls from initial level.
  02=4022×10×H
H=160020=80m
Hence, maximum height reach by centre of mass from ground level will be
hmax=(hcm)initial+H=20+80=100m

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