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

Question

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

Tardigrade Admin · Accepted Answer

W=∫ limitsrgriF. dr W=∫ limits01 -xdx +∫ limits10ydy W=(-x2/2)|01+(y2/2)|10 =((02/2)-(12/2))+((12/2)-(02/2)) W=1 J

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

$\frac{3}{2}$

$2$

$1$

$\frac{1}{2}$

$W = r_{i} \int r_{g} F . d r$
$W = 1 \int 0 - x d x +$ $0 \int 1 y d y$
$W = \frac{- x ^{2}}{2} ∣ ∣_{_{_{1}}}^{^{0}} + \frac{y ^{2}}{2} ∣ ∣_{_{_{0}}}^{^{1}}$
$= (\frac{0 ^{2}}{2} - \frac{1 ^{2}}{2}) + (\frac{1 ^{2}}{2} - \frac{0 ^{2}}{2})$
$W = 1 J$

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

23​

2

1

21​

W=ri​​∫rg​​​F.dr W=1∫0​−xdx+0∫1​ydy W=2−x2​∣∣​1​​0​+2y2​∣∣​0​​1​ =(202​−212​)+(212​−202​) W=1J

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

$\frac{3}{2}$

$2$

$1$

$\frac{1}{2}$

$W = r_{i} \int r_{g} F . d r$
$W = 1 \int 0 - x d x +$ $0 \int 1 y d y$
$W = \frac{- x ^{2}}{2} ∣ ∣_{_{_{1}}}^{^{0}} + \frac{y ^{2}}{2} ∣ ∣_{_{_{0}}}^{^{1}}$
$= (\frac{0 ^{2}}{2} - \frac{1 ^{2}}{2}) + (\frac{1 ^{2}}{2} - \frac{0 ^{2}}{2})$
$W = 1 J$