You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Introducing Flux

Given F⃗ = ...

Question

Given $\to F = (x y^{2})^i + (x^{2} y)^j$ N. The work done by $\to F$ when a particle is take along the semicircular path OAB where the coordinates of B are (4, 0) is

\frac{65}{3} J

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{75}{2} J

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{73}{4} J

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Zero

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D Zero
Given $\to F = (x y^{2})^i + (x^{2} y)^j$
$W = \int F_{x} d x + \int F_{y} d y = \int x y^{2} d x + \int x^{2} y d y$
$= \frac{1}{2} \int d (x^{2} y^{2}) = {[\frac{x^{2} y^{2}}{2}]}_{(0, 0)}^{(4, 0)} = 0$

Suggest Corrections

Similar questions

Given $\to F = (x y^{2})^i + (x^{2} y)^j N$ . The work done by $\to F$ when a particle is taken along the semicircular path OAB where the coordinates of B are (4,0) is

Q. A particle is moved along the different paths OAC, OBC & ODC as shown in the fig. Path ODC is a parabola,

y = 4 x^{2}

. Find the work done by a force

\to F = x y^i + x^{2} y^j

on the particle along these paths. Is this force a conservative force?

Q. A particle of mass

m

moves along the quarter section of the circular path whose centre is at the origin. The radius of the circular path is

a

. A force

\to F = y^i - x^j

newton acts on the particle, where

x, y

denote the coordinates of position of the particle. The work done by this force in taking the particle from point A (

a, 0

) to point B (

0, a

) along the circular path is

Q. A particle has initial velocity

\to v = 3 i + 4 j

, and a constant force

\to F = - 4 i + 3 j

acts on a particle. The path of the particle is

Join BYJU'S Learning Program

Given →F=(xy2)^i+(x2y)^j N. The work done by →F when a particle is take along the semicircular path OAB where the coordinates of B are (4, 0) is

The correct option is D ZeroGiven →F=(xy2)^i+(x2y)^jW=∫Fxdx+∫Fydy=∫xy2dx+∫x2ydy=12∫d(x2y2)=[x2y22](4,0)(0,0)=0

Given $\to F = (x y^{2})^i + (x^{2} y)^j$ N. The work done by $\to F$ when a particle is take along the semicircular path OAB where the coordinates of B are (4, 0) is

The correct option is D Zero
Given $\to F = (x y^{2})^i + (x^{2} y)^j$
$W = \int F_{x} d x + \int F_{y} d y = \int x y^{2} d x + \int x^{2} y d y$
$= \frac{1}{2} \int d (x^{2} y^{2}) = {[\frac{x^{2} y^{2}}{2}]}_{(0, 0)}^{(4, 0)} = 0$