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Question: Answered & Verified by Expert
A block of mass M is placed on a smooth horizontal surface and it is pulled by a light spring as shown in the diagram. If the ends A and B of the spring are moving with 4 m s-1 and 2 m s-1 respectively and the rate at which spring energy is increasing is 20 J s-1. then what is the value of spring force (in N)?

PhysicsOscillationsJEE Main
Solution:
1396 Upvotes Verified Answer
The correct answer is: 10
Let, distance moved by A and B in any time interval as measured from natural length of spring are xA and xB respectively. Let, l is the natural length of spring, then elongation in spring at any instant is

                x=xA-xB-l

                U = kx 2 2

              dU dt = P = k 2 × 2 x dx dt

⇒         2 0 = kx  v A - v B

⇒         kx = 2 0 4 - 2 = 1 N

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