An object is displaced from position vector r 1-2 -3 - m to r 2-4 -6 - m under the action of a force F -3 x 2-2 y - N- Find thework done by this force- A- 17 JB- 10 JC- 83 JD- 80 J

An object has a displacement from position vector $_{1} = (2^i + 3^j) m$
to $_{2} = (4^i + 6^j) m$ under a force $\to F = (3 x^{2}^i + 2 y^j) N,$ then work done by the force is:

Q. An object is displaced from position vector

_{1} = (2^i + 3^j)

m

_{2} = (4^i + 6^j)

m

under a force

\to F = (3 x^{2}^i + 2 y^j)

N

. Find the work done.

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An object is displaced from position vector →r1=(2^i+3^j) m to →r2=(4^i+6^j) m under the action of a force →F=(3x2^i+2y^j) N. Find the work done by this force.

The correct option is B 83 JWprk done by variable forceW=r2∫r1→F.→dr=r2∫r1(3x2^i+2y^j).(dx^i+dy^j+dz^k) =r2∫r1(3x2 dx+2y dy)=[x3+y2](4,6)(2,3)=83 J

An object is displaced from position vector ${\to r}_{1} = (2^i + 3^j) m$ to ${\to r}_{2} = (4^i + 6^j) m$ under the action of a force $\to F = (3 x^{2}^i + 2 y^j) N$ . Find the work done by this force.

The correct option is B $83 J$
Wprk done by variable force $W = r_{2} \int r_{1} \to F . \to d r = r_{2} \int r_{1} (3 x^{2}^i + 2 y^j) . (d x^i + d y^j + d z^k)$
$= r_{2} \int r_{1} (3 x^{2} d x + 2 y d y) = [x^{3} + y^{2}]_{(2, 3)}^{(4, 6)} = 83 J$