Physics

Problem

At a distance of

2.0\times10^{5}\,\text{m}

from the centre of a certain asteroid (mass

5.0\times10^{12}\,\text{kg}

), the gravitational field intensity is

E_1

. At what distance from the asteroid’s centre will the field intensity be

2E_1

? a)

1.0\times10^{5}\,\text{m}

1.6\times10^{5}\,\text{m}

1.4\times10^{5}\,\text{m}

2.8\times10^{5}\,\text{m}

Intuitive explanation

Gravitational field intensity follows an inverse-square law: it drops as $1/r^2$ . To double the field strength, you need to move closer to the source—specifically, you'll need to reduce your distance by a factor that makes $r^2$ shrink by half. Think about how the denominator in $E = GM/r^2$ must change to produce twice the value.

Intuitive explanation

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