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Standard X

Physics

Newton's Universal Law of Gravitation

If two bodies...

Question

If two bodies have a mass ratio of 1 : 2, what is the ratio of their accelerations due to gravitational force applied on each other?

1 : 2

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2 : 3

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1 : 4

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2 : 1

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Solution

The correct option is D 2 : 1
Gravitational force by one body on other,
$F = \frac{G M m}{d^{2}}$
Acceleration of body of mass M = $\frac{F}{M} = \frac{G m}{d^{2}}$
Acceleration of body of mass m = $\frac{F}{m = \frac{GM}{d^{2}}}$
Given that m : M = 1 : 2
Ratio of acceleration = $\frac{F / m}{F / M = M : m = 2 : 1}$

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If two bodies have a mass ratio of 1 : 2, what is the ratio of their accelerations due to gravitational force applied on each other?

The correct option is D 2 : 1Gravitational force by one body on other, F = GMm/d2 Acceleration of body of mass M = F/M = Gm/d2 Acceleration of body of mass m = F/m = GM/d2 Given that m : M = 1 : 2 Ratio of acceleration = F/m/F/M = M:m = 2:1