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- - 3x2 - - 2y - N- Find the work done by this force-

The correct option is D 83 J W = ∫_r⃗_⃗1⃗^r⃗_⃗1⃗ F⃗ · d⃗r = ∫_r⃗_⃗1⃗^r⃗_⃗2⃗ (3x^2 î + 2y ĵ) · (dx î + dy ĵ + dz k̂) = #160; #160; ...

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Standard XII

Physics

Displacement

An object is ...

Question

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

69 J

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76 J

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97 J

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83 J

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Solution

The correct option is D $83 J$
$W = \int_{_{1}}^{_{1}} \to F \cdot \to d r = \int_{_{1}}^{_{2}} (3 x^{2}^i + 2 y^j) \cdot (d x^i + d y^j + d z^k)$

$= \int_{_{1}}^{_{2}} (3 x^{2} d x + 2 y d y) = [x^{3} + y^{2}]_{(2, 3)}^{(4, 6)} = 83 J$ .

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Similar questions

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

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

. Find the work done in joules by this force.

Q. An object is displaced from position vector

{\to r}_{1} = (2^i + 3^j) m

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

m under a force

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

Find the work done by this force.

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.

Q. An object is displaced from position vector

{\to r}_{1} = (2^i + 3^j) m

{\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.

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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 D 83JW=∫→r1→r1→F⋅→dr=∫→r2→r1(3x2^i+2y^j)⋅(dx^i+dy^j+dz^k)=∫→r2→r1(3x2dx+2ydy)=[x3+y2](4,6)(2,3)=83J.

An object is displaced from position vector $_{1} = (2^i + 3^j) m$ to $_{2} = (4^i + 6^j) m$ 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 D $83 J$
$W = \int_{_{1}}^{_{1}} \to F \cdot \to d r = \int_{_{1}}^{_{2}} (3 x^{2}^i + 2 y^j) \cdot (d x^i + d y^j + d z^k)$

$= \int_{_{1}}^{_{2}} (3 x^{2} d x + 2 y d y) = [x^{3} + y^{2}]_{(2, 3)}^{(4, 6)} = 83 J$ .