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Question

# The gravitational field in a region is given by ¯E=(4^i+^j)N/kg. Work done by this field is zero when a particle is moved along the line.

A

y+4x=2

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B

4y+x=6

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C

x+y=5

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D

All of these

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Solution

## The correct option is A y+4x=2 Work done will be zero when displacement is perpendicular to the field. The field makes an angle θ1=tan−1(14) with positive x-axis While the line y + 4x = 2 makes and angle θ2=tan−1(−4) with positive x-axis ∴ θ1+θ2=90∘ i.e., the line y + 4x = 2 is perpendicular to ¯E.

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