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Question

The gravitational field in a region due to a certain mass distribution is given by E=(4^i3^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 J
Given that,
Gravitational field, E=(4^i3^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^i3^j) Nkg
r=((232)^i+(21)^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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