A force F=A y2+B y+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

Question

A force F=A y2+B y+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) (2 A a5/3) (B) (2 A a5/3)+2 C a (C) (2 A a5/3)+(B a2/2)+C a (D) None of these

Tardigrade Admin · Accepted Answer

W=∫ F d y=∫ limits-a+a(A y2+B y+C) d y [(A y3/3)+(B y2/2)+C y]-a+a =[(A a3/3)+(B a2/2)+C a]-[-(A a3/3)+(B a2/2)-C a] =(2 A a3/3)+2 C a

Q. A force $F = A y^{2} + B y + C$ acts on a body in the $y$ -direction. The work done by this force during a displacement from $y = - a$ to $y = a$ is

$\frac{2 A a ^{5}}{3}$

$\frac{2 A a ^{5}}{3} + 2 C a$

$\frac{2 A a ^{5}}{3} + \frac{B a ^{2}}{2} + C a$

None of these

$W = \int F d y = - a \int + a (A y^{2} + B y + C) d y$
$[\frac{A y ^{3}}{3} + \frac{B y ^{2}}{2} + C y]_{- a}^{+ a}$
$= [\frac{A a ^{3}}{3} + \frac{B a ^{2}}{2} + C a] - [- \frac{A a ^{3}}{3} + \frac{B a ^{2}}{2} - C a]$
$= \frac{2 A a ^{3}}{3} + 2 C a$

Q. 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

32Aa5​

32Aa5​+2Ca

32Aa5​+2Ba2​+Ca