Physics
Mechanics
Easy

Question

A string is wrapped several times on a cylinder of mass M and radius R. the cylinder is pivoted about its axis of symmetry. A block of mass m tied to the string rests on a support so that the string is slack. the block is lifted up to a height h and the support is removed. (shown in figure)

When the string experience a jerk, a large impulsive force is generated for a short duration, so that contribution of weight mg can be neglected during this duration. Then what will be speed of block m, just after string has become taut

  1. fraction numerator square root of 2 g h end root over denominator open square brackets 1 plus M over m close square brackets end fraction
  2. fraction numerator square root of 2 g h end root over denominator open square brackets 1 plus fraction numerator M over denominator 2 m end fraction close square brackets end fraction
  3. fraction numerator square root of g h end root over denominator open square brackets 1 plus M over m close square brackets end fraction
  4. fraction numerator square root of g h end root over denominator open square brackets 1 plus fraction numerator M over denominator 2 m end fraction close square brackets end fraction

The correct answer is: fraction numerator square root of 2 g h end root over denominator open square brackets 1 plus fraction numerator M over denominator 2 m end fraction close square brackets end fraction


    When the string experiences a jerk, the large impulse developed is of very short duration so that the contribution of weight mg can be neglected during this time interval.
    The angular momentum of the system is conserved, as the tension is internal force for the  system
    Error converting from MathML to accessible text.

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