Physics-
General
Easy

Question

In the given figure four identical spheres of equal mass m are suspended by wires of equal length l subscript 0 end subscript, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is

  1. square root of 2 g l subscript 0 end subscript end root    
  2. square root of 3 g l subscript 0 end subscript end root    
  3. square root of g l subscript 0 end subscript end root    
  4. square root of fraction numerator g l subscript 0 end subscript over denominator 2 end fraction end root    

The correct answer is: square root of 2 g l subscript 0 end subscript end root


    When the sphere 1 is released from horizontal position, then from energy conservation, potential energy at height l subscript 0 end subscript equals kinetic energy at bottom
    Or m g l subscript 0 end subscript equals fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent
    Or v equals square root of 2 g l subscript 0 end subscript end root
    Since, all collisions are elastic, so velocity of sphere 1 is transferred to sphere 2, then from 2 to 3 and finally from 3 to 4. Hence, just after collision, the sphere 4 attains a velocity equal to square root of 2 g l subscript 0 end subscript end root

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