Question

# Two balls A and B of equal masses are projected upward simultaneously, one from the ground with speed 50 ms−1 and other from height 40 m above the first ball high tower with initial speed 30 ms−1. Find the maximum height attained by their centre of mass.

A
80 m
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B
100 m
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C
20 m
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D
60 m
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Solution

## The correct option is C 100 mThe initial position of centre of mass is ycm=m×0+m×402m=20m Initial velocity of centre of mass ucm=m×50+m×302m=40ms−1 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=402−2×10×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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