JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Work, Power & Energy

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A particle of mass 10 g moves in a straight line with retardation 2 x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is

(\frac{10}{x})^{- n}

J. The value of

n

will be

Answer: 2

Solution

Loss of kinetic energy equals work done against the retarding force.

Retarding force:

F = ma = m (2 x) = 2 m x

Work done:

W = \int_{0}^{x} F d x = \int_{0}^{x} 2 m x d x = m x^{2}

With

m = 10

= 1 0^{- 2}

kg:

W = 1 0^{- 2} x^{2}

= (\frac{10}{x})^{- 2}

J

Comparing with the given form,

n = 2

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Integer answer

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