NTA Abhyas JEE Main2020PhysicsWork, Power and EnergyPractice
A particle of mass m moves along the quarter section of the circular path whose centre is at the origin. The radius of the circular path is a . A force F → = y i ^ - x j ^ N acts on the particle, where x , y denote the coordinates of the position of the particle. Calculate the work done by this force in taking the particle from point A ( a , 0 ) to point B ( 0 , a ) along the circular path.
Options
- Aπa 2   J
- Bπa 2 2   J
- C- πa 2 2 J
- DZero
Correct answer
C. - πa 2 2 J
Step-by-step solution
Work done by force F; w = ∫ F → . d r = ∫ y i ^ - x j ^ . ( d x i ^ + d y j ^ )   = ∫ y d x - x d y ∵ x 2 + y 2 = a 2 ∴ x d x + y d y = 0 ⇒ W = ∫ y - y d y x - x d y = - ∫ x 2 + y 2 x d y = - ∫ 0 a a 2 a 2 - y 2 d y = - π a 2 2