A variable force F acts along the x -axis given by F=(3 x2 - 2 x + 1) N . The work done by the force when a particle of mass 100 g moves from x=50 cm to x=100 cm is

Question

A variable force F acts along the x -axis given by F=(3 x2 - 2 x + 1) N . The work done by the force when a particle of mass 100 g moves from x=50 cm to x=100 cm is (A) 0.625 J (B) 6.25 J (C) 0.0625 J (D) 62.5 J

Tardigrade Admin · Accepted Answer

xi n i t i a l=50 cm xf i n a l=100 cm Therefore work done by the variable force, W= displaystyle ∫ xi n i t i a lxf i n a l F . d x W= displaystyle ∫ 0.51 (3 x2 - 2 x + 1) d x W=[x3 - x2 + x]0.51 W=(1 - 0 . 53)-(1 - 0 . 52)+(1 - 0.5) W=0.875-0.75+0.5 W=0.625 J

Q. A variable force $F$ acts along the $x$ -axis given by $F = (3 x^{2} - 2 x + 1) N$ . The work done by the force when a particle of mass $100 g$ moves from $x = 50 c m$ to $x = 100 c m$ is

$0.625 J$

$6.25 J$

$0.0625 J$

$62.5 J$

Q. A variable force F acts along the x -axis given by F=(3x2−2x+1)N . The work done by the force when a particle of mass 100g moves from x=50cm to x=100cm is

0.625J

6.25J

0.0625J

62.5J

xinitial​=50cm xfinal​=100cm Therefore work done by the variable force, W=∫xinitial​xfinal​​F.dx W=∫0.51​(3x2−2x+1)dx W=[x3−x2+x]0.51​ W=(1−0.53)−(1−0.52)+(1−0.5) W=0.875−0.75+0.5 W=0.625J

Q. A variable force $F$ acts along the $x$ -axis given by $F = (3 x^{2} - 2 x + 1) N$ . The work done by the force when a particle of mass $100 g$ moves from $x = 50 c m$ to $x = 100 c m$ is

$0.625 J$

$6.25 J$

$0.0625 J$

$62.5 J$