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Consider a force overset ( r)(F)= -x^(3)...

Consider a force `overset ( r)(F)= -x^(3) hat( i) +y^(2) hat(j) `.The work done by this force in moving a particle from A(1,0) to B(0,1) along a straight line is `:` ( All quantities are in SI units )

A

1

B

`(5)/(12)`

C

`( 7)/( 12) `

D

`( 3)/( 4)`

Text Solution

Verified by Experts

`overset(1) (d)overset(1) (r ) =dx hat(i) + dy hat(j) `, `int overset( r )( F ) . overset( 1)(d) overset(1) (r) = underset(0)overset(1)int-x^(3) .dx+ underset(0)overset(1)(int)y^(2)dy = (-x^(4))/( 4) underset(1)overset(1)(|)+(y^(3))/( 3) underset(0)overset(1) (|) = (1)/(4) + (1)/(3) =(7)/( 12) J`
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