Question

A force F = Ay² + By + C acts on a body in the y-direction. The work done by this force during a displacement from y = – a to y = a is 

(A) [{2Aa³} / 3] 

(B) [{2Aa³} / 3] + 2ca 

(C) [{2Aa³} / 3] + [{Ba²} / 2] + ca 

(D) None of these.

Answer 1

Correct option: (B) [{2Aa³} / 3] + 2ca

Explanation:

W = F × s

= ∫ F ∙ dy

= +a∫y=–a (Ay2 + By + C) dy

= [{(Ay³) / 3} + {(By²) / 2} + cy]^a_–a 

= (A/3) (a³ + a³) + (B/2) (a² – a²) + C(a + a)

= [{2Aa³} / 3] + 2ac