A force field has components Fₓ = 2xy and Fᵧ = x². A particle moves from (0,0) to (2,4) along the path y = x². If the work done is N joule, find N.
Physics · Work , Power and Energy · question based on work
JEE Mains NEET JEE Advanced

Question

A force field has components Fₓ = 2xy and Fᵧ = x². A particle moves from (0,0) to (2,4) along the path y = x². If the work done is N joule, find N.

G1 Physics · Accepted Answer

Along y = x², dy = 2x dx. Thus dW = Fₓ dx + Fᵧ dy = 2x(x²)dx + x²(2x dx) = 4x³ dx. Hence W = ∫₀²4x³dx = [x⁴]₀² = 16 J.