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In a game house the above punch bag has the shown set up. If you punch the bag at mean position and it gets compressed by a distance x m, then it will come back to mean and get elongated by the same distance x m. Rohit punches the bag and compresses it by 5 cm. What is the magnitude of maximum displacement (M) and magnitude of minimum displacement (m)?


A

M = +5 m, m = -5 m

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B

M = +5 m, m = +5 m

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C

M = + 5 m = 0

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D

M = 0, m = 5

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Solution

The correct option is B

M = + 5 m = 0


Step 1: Fix the starting position - Mean position (0, 0)

Now for maximum displacement the finishing position should be as far as possible from the mean which can either be the maximum compressed position or the maximum elongated position which doesn't matter. Why?

In compressed position displacement is 5 cm to left from the mean. Our convention says to take it as -5m, where negative sign is only there for direction. When the bag is at 5 cm to the right (elongated position) by sign convention it's at +5 m but the + sign only shows direction that the bag is right of origin . So magnitude of maximum displacement can be either in maximum compressed or elongated position.

Magnitude of minimum displacement is 0 , when the bag after being compressed starts towards the mean position. At this point when it reaches mean position the shortest distance between initial and final position is 0. So the magnitude of minimum displacement is 0 m.


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