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 (10/x)⁻ⁿ J. The value of n will be __________

Solution

Physics sir · 4 steps

The retarding force grows with x, so integrate it to get the work. That work is the kinetic energy lost.

1. Retarding force. Mass m = 10 g = 0.01 kg. The retardation is 2x, so the force opposing the motion is F = m × 2x = 0.02x newton.
2. Work-energy theorem. The loss of kinetic energy equals the work done against this force. The force changes with x, so you have to integrate from 0 to x.

   Δ K = ∫₀ˣ 0.02x dx = 0.01x² = x²/100

3. Match the form. Write x²/100 = (x/10)² = (10/x)⁻². Compare this with (10/x)⁻ⁿ.
4. So. -n = -2, which gives n = 2.

The common slip: -2. Matching (x/10)² to the exponent without flipping the fraction gives -2. The given form has 10/x raised to -n, so n = 2.

The idea to keep. When force depends on position, work is ∫ F dx, not force times distance. Convert grams to kilograms before you integrate.

Answer from the NTA final answer key. Solution by PrepWiser.