Q36 / 92 · NTA Abhyas (JEE Main) 2020 · Physics · Work Power Energy

The power supplied by a force acting on a particle moving in a straight line is constant. The velocity of the particle varies with the displacement x as

  • A
    x⁡ 1 / 2
  • B
    x⁡
  • C
    x⁡ 2
  • Correct answer
    D
    x⁡ 1 / 3

Solution

P⁡ = F v⁡ = ma v⁡ = m⁡ d⁡ 2 x⁡ d⁡ t⁡ 2 d⁡ x⁡ d⁡ t⁡

Since, power is constant

d⁡ 2 x⁡ d⁡ t⁡ 2 d⁡ x⁡ d⁡ t⁡ = k⁡

or  d⁡ d⁡ t⁡ d⁡ x⁡ d⁡ t⁡ 2 = k⁡

d⁡ x⁡ d⁡ t⁡ 2 = k⁡ 1 t⁡

d⁡ x⁡ d⁡ t⁡ = k⁡ 1 t⁡

d⁡ x⁡ d⁡ t⁡ = k⁡ 2 t⁡ 1 / 2    ∵ k⁡ 1 1 / 2 = k⁡ 2

x⁡ = k⁡ 3 t⁡ 3 / 2    ∵ k⁡ 3 = 2 3 k⁡ 2

Hence  d⁡ x⁡ d⁡ t⁡ ∝ t⁡ 1 / 2 ∝ x⁡ 1 / 3

Hence, the correct answer is option: 'D'.

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