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MHT CET2017PhysicsLaws of Motion

An elevator of mass m is connected to a rope which pulls the elevator up with a maximum acceleration equal to a . If the maximum bearable tension in the rope is T , then for a safe journey the minimum diameter of the rope is [ g = acceleration due to gravity]

Options

  1. A2 m g + a π T 1 2
  2. B4 m g + a π T 1 2
  3. Cm g + a π T 1 2
  4. Dm g + a 2 π T 1 2

Correct answer

B. 4 m g + a π T 1 2

Step-by-step solution

The maximum tension in the rope = m ( g + a ) Stress in the rope = m g + a π r 2 ∴ T = m g + a π r 2 = m g + a π d 2 2 ∴ T = 4 m g + a π d 2 ∴ d 2 = 4 m g + a π T ∴ d = 4 m g + a π T 1 2

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