Two objects attract each other with a gravitational force of magnitude 9.90 x 10

Question

Two objects attract each other with a gravitational force of magnitude 9.90 x 10 N when separated by 20.0 cm. If the total mass of the two objects is 5.05 kg, what is the mass of each? 3.34 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. carry out all intermediate results to at least four-digit accuracy to minimize roundoff error kg heavier mass) 1.71 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. kg (lighter mass) s within 1

Explanation / Answer

Given,

F = 9.9 x 10^-9 N ; r = 20 cm = 0.2 m ; Mt = 5.05 kg

We know that the force of attraction between two objects is given by:

F = Gm1m2/r^2

6.67 x 10^-11 x m1m1/0.2^2 = 9.9 x 10^-9

m1m2 = 0.2^2 x 9.9 x 10^-9/(6.67 x 10^-11) = 5.94

m1 = 5.94/m2

we have, Mt = m1 + m2 = 5.05 kg

5.94/m2 + m2 = 5.05

m2^2 - 5.05 m2 + 5.94 = 0

solving this quadratic eqn we get

m2 = 3.18 kg and 1.86 kg

Hence, m1 = 1.86 and m2 = 3.18 kg

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