A body is displaced from (.0,0.) to (.1 m,1 m.) along the path x=y by a force overset arrow F=(.y hati+x2 hatj.) N , then the work done by the force is

Question

A body is displaced from (.0,0.) to (.1 m,1 m.) along the path x=y by a force overset arrow F=(.y hati+x2 hatj.) N , then the work done by the force is (A) (4/3)J (B) (5/6)J (C) (3/2)J (D) (7/5)J

Tardigrade Admin · Accepted Answer

W= displaystyle ∫ (. 0,0 .)(. 1,1 .) overset arrow F . overset arrow d x Here overset arrow ds=dx hati+ dy hatj + dz hatk ∴ W= displaystyle ∫ (. 0,0 .)(. 1,1 .) (. x2 d y + y d x .) = displaystyle ∫ (. 0,0 .)(. 1,1 .) (. x2 d y + x . d x .) (As x=y ) ∴ W=([(y3/3) + (x2/2)])(. 0,0 .)(. 1,1 .)=(5/6)J

Q. A body is displaced from $(0, 0)$ to $(1 m, 1 m)$ along the path $x = y$ by a force $F \to = (y \hat{i} + x^{2} \hat{j}) N$ , then the work done by the force is

$\frac{4}{3} J$

$\frac{5}{6} J$

$\frac{3}{2} J$

$\frac{7}{5} J$

Q. A body is displaced from (0,0) to (1m,1m) along the path x=y by a force F→=(yi^+x2j^​)N , then the work done by the force is

34​J

65​J

23​J

57​J

W=∫(0,0)(1,1)​F→.d→x Here d→s=dxi^+dyj^​+dzk^ ∴W=∫(0,0)(1,1)​(x2dy+ydx) =∫(0,0)(1,1)​(x2dy+x.dx) (As x=y ) ∴W=([3y3​+2x2​])(0,0)(1,1)​=65​J

Q. A body is displaced from $(0, 0)$ to $(1 m, 1 m)$ along the path $x = y$ by a force $F \to = (y \hat{i} + x^{2} \hat{j}) N$ , then the work done by the force is

$\frac{4}{3} J$

$\frac{5}{6} J$

$\frac{3}{2} J$

$\frac{7}{5} J$