Consider a force F=-x hati+y hatj. The workdone by this force in moving a particle from point P(1,0) to Q(0,1) along the line segment is (all quantities are in SI units).

Question

Consider a force F=-x hati+y hatj. The workdone by this force in moving a particle from point P(1,0) to Q(0,1) along the line segment is (all quantities are in SI units). (A) (1/2) J (B) 1 J (C) (3/2) J (D) zero

Tardigrade Admin · Accepted Answer

Work done, W=∫ vecF ⋅ d s=(-x hati × y hatj) ⋅(x hati+y hatj) ⇒ W=∫ limits10 x d x+∫ limits01 y d y=(0+(1/2))+(1/2)=1 J

Q. Consider a force $F = - x \hat{i} + y \hat{j}$ . The workdone by this force in moving a particle from point $P (1, 0)$ to $Q (0, 1)$ along the line segment is (all quantities are in SI units).

$\frac{1}{2} J$

$1 J$

$\frac{3}{2} J$

zero

Work done, $W = \int F \cdot d s = (- x \hat{i} \times y \hat{j}) \cdot (x \hat{i} + y \hat{j})$
$\Rightarrow W = 1 \int 0 x d x + 0 \int 1 y d y = (0 + \frac{1}{2}) + \frac{1}{2} = 1 J$

Q. Consider a force F=−xi^+yj^​. The workdone by this force in moving a particle from point P(1,0) to Q(0,1) along the line segment is (all quantities are in SI units).

21​J

1J

23​J