A force F -4 xi -2 y - displaces a body from r 1-3 -8 - to r 2-9 -6 - Find the work done by the force-A- 125 JB- 120 JC- 116 JD- Zero

Gives force =F = 4x î + 2yĵ initial position r_1 = 3î + 8ĵ and portion r_2 = 9î 6ĵ We know work done W = ∫^s_2_s1F. ds = ∫^s_2_s_1F.(dx î + dyĵ) W = ∫^s_2_s1 ...

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Byju's Answer

Standard XII

Physics

Work Done as Dot Product

A force F =4 ...

Question

A force $\to F = 4 x^i + 2 y^j$ displaces a body from $r_{1} = 3^i + 8^j$ to $_{2} = 9^i - 6^j$ . Find the work done by the force.

125 J

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120 J

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116 J

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Solution

The correct option is C $116 J$
Gives force $= \to F = 4 x^i + 2 y^j$
initial position $_{1} = 3^i + 8^j$
and portion $_{2} = 9^i - 6^j$
We know work done
$W = \int_{s 1}^{s_{2}} \to F . d \to s$
$= \int_{s_{1}}^{s_{2}} \to F . (d x^i + d y^j)$
$W = \int_{s 1}^{s_{2}} (4 x^i + 2 y^j) . (d x^i + d y^j)$
$= \int_{3}^{9} 4 x d x + \int_{8}^{- 6} 2 y d y$
$W = [2 x^{2}]_{3}^{9} + [y^{2}]_{8}^{- 6}$
$W = 144 + (- 28)$
$W = 116 J$

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Similar questions

Q. A force

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An object is displaced from position vector $_{1} = 2^i + 3^j (m)$ to $_{2} = 4^j + 6^k (m)$ under a force

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A force →F=4x^i+2y^j displaces a body from r1=3^i+8^j to →r2=9^i−6^j. Find the work done by the force.

The correct option is C 116 JGives force =→F=4x^i+2y^j initial position →r1=3^i+8^j and portion →r2=9^i−6^j We know work done W=∫s2s1→F.d→s =∫s2s1→F.(dx^i+dy^j) W=∫s2s1(4x^i+2y^j).(dx^i+dy^j) =∫934xdx+∫−682ydy W=[2x2]93+[y2]−68 W=144+(−28) W=116 J

A force $\to F = 4 x^i + 2 y^j$ displaces a body from $r_{1} = 3^i + 8^j$ to $_{2} = 9^i - 6^j$ . Find the work done by the force.