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Question

The 2 kg block shown in figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness 5 N/m.

The cord hinged at O is initially unstretched and always remains elastic. The block is given a velocity v of 1.5 m/s perpendicular to the cord. The magnitude of velocity in m/s of the block at the instant the cord is stretched by 0.4 m is

Options :

  1. 0.83

  2. 1.07

  3. 1.36

  4. 1.50

Show Answer

Answer :

1.36

Solution :

Given, Mass of block (m) = 2 kg, Rod stiffness (k) = 5 N/m, Change in length of rod (x) = 0.4 m

v1 = initial velocity = 1.5 m/s and let v2 be the final velocity

Using conservation of energy

1 2 m v 1 2 = 1 2 m v 2 2 + 1 2 k x 2

1 2 × 2 × ( 1.5 ) 2 = 1 2 × 2 × V 2 2 + 1 2 × 5 × ( 0.4 ) 2

v2 = 1.36 m/s

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