The gravitational potential in a region is given by, $V = 20 (x + y) J / k g$ . Find the magnitude of the gravitational force on a particle of mass $0.5 k g$ placed at the origin.

10

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20

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10 \sqrt{2}

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20 \sqrt{2}

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Solution

The correct option is C $10 \sqrt{2}$ N
We know that from definition,

$E = - (\frac{\partial V}{\partial x} i + \frac{\partial V}{\partial x} i + \frac{\partial V}{\partial x} i)$

Thus,

$E = (20 i + 20 j) N / k g$

Thus, force is

$F = m E = 0.5 (20 i + 20 j) = (10 i + 10 j) N$

Magnitude of force is $10 \sqrt{2} N$

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The gravitational potential in a region is given by, V=20(x+y)J/kg. Find the magnitude of the gravitational force on a particle of mass 0.5kg placed at the origin.

The correct option is C 10√2 NWe know that from definition,E=−(∂V∂xi+∂V∂xi+∂V∂xi)Thus, E=(20i+20j)N/kgThus, force isF=mE=0.5(20i+20j)=(10i+10j)NMagnitude of force is 10√2N

The gravitational potential in a region is given by, $V = 20 (x + y) J / k g$ . Find the magnitude of the gravitational force on a particle of mass $0.5 k g$ placed at the origin.