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For conservative of U w.r.t. x keeping y...

For conservative of U w.r.t. x keeping y and z constant and so on.
`{:(,"Column-I",,,"Column-II"),((A),"For" U=x^(2) yz"," at (5, 0,0),,(P),F_(x)=0),((B),"For" U=x^(2)+yz at (5, 0, 0),,(Q),F_(y)=0),((C),"For" U=x^(2)(y+z) at (5, 0, 0),,(R),F_(z)=0),((D),"For" U=x^(2)y+z at (5, 0,0),,(S),U=0):}`

Text Solution

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The correct Answer is:
A-P,Q,R,S; B-Q, R; C-P,S; D-P, S
For (A) : `vec(F)=-2xyz hat(i)-x^(2)zhat(j)-x^(2)yhat(k) rArr F_(x)=0, F_(y)=0, F_(z)=0, U=0`
For (B): `vec(F)=-2xhat(i)-zhat(j)-yhat(k)rArr F_(x) ne 0, F_(y)=0, F_(z)=0, U ne 0`
For (C) : `vec(F)=-2x(y+z)hat(i)-x^(2)hat(j)-x^(2)hat(k)rArr F_(x)=0, F_(y) ne 0, F_(z) ne 0, U=0`
For (D) : `vec(F)=-2xy hat(i)-x^(2)hat(j)-hat(k)rArr F_(x)=0, F_(y) ne 0, F_(z) ne 0, U=0`
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