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Question

# The gravitational field in a region due to a certain mass distribution is given by →E=(4^i−3^j) N/kg. The work done by the field in moving a particle of mass 2 kg from (2 m,1 m) to (23 m,2 m) along the line 3x+4y=10 is

A
253 J
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B
503 J
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C
253 J
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D
Zero
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Solution

## The correct option is B −503 JGiven that, Gravitational field, →E=(4^i−3^j) N/kg Initial position of partical, Pi=(2 m,1 m) Final position of particle, Pf=(23 m,2 m) Equation of line is 3x+4y=10 The relation between gravitational field and potetial is Potential Difference, dV=−∫→E.→dr Since →E is constant, ΔV=−→E.∫→dr=−→E.→r →E=(4^i−3^j) Nkg →r=((23−2)^i+(2−1)^j) m →r=(−43^i+^j) m ⇒−→E.→r=(−4^i+3^j).(−43^i+^j) ⇒ΔV=−→E.→r=163+3 ⇒ΔV=−→E.→r=253 The work done by gravitational force does not depend on path, it depends on the initial and final position only. Work done = Change in potential energy mΔV=2×253=503 J Key Concept: When field vector is constant, V=−→E.→r

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