A particle of mass 10 g moves in a straight line with retardation 2x, where x is displacement in SI units. Its loss of kinetic energy for the displacement is (10/x)⁻ⁿ J. The value of n is ______.
Physics · Circular Motion
JEE Mains 6 April 2023 Shift 1 Morning Shift

Question

A particle of mass 10 g moves in a straight line with retardation 2x, where x is displacement in SI units. Its loss of kinetic energy for the displacement is (10/x)⁻ⁿ J. The value of n is ______.

G1 Physics · Accepted Answer

Retardation magnitude is given by a = 2x Using v(dv/dx) = a and taking retardation opposite to motion: v dv/dx = −2x Multiply by mass m = 10 g = 0.01 kg: m v dv = −2mx dx The loss of kinetic energy over displacement x is therefore proportional to x². Thus the required power of x corresponds to n = 2. Final value: 2