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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 )?

Correct answer

10

Step-by-step solution

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 = x A - x B - 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 0  N

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