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Question

The gravitational field in a region is given by →g=[4^i+^j] N kg−1. Work done by this field is zero when the particle moves along the line (Choose the appropriate option)

A
y+4x=2
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B
4y+x=2
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C
x+y=5
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D
All of the above
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Solution

The correct option is A y+4x=2Work done is zero when the displacement is perpendicular to the field. The field makes, θ1=tan−1[14] with positive X− axis. While the line y+4x=2 makes the angle, θ2=tan−1[−4] with positive X− axis. As θ1+θ2=90∘ i.e., the line y+4x=2 is perpendicular to →g

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