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Cerrena [4.2K]
3 years ago
11

Two objects attract each other with a gravitational force of magnitude 1.01 10-8 N when separated by 19.9 cm. If the total mass

of the two objects is 5.11 kg, what is the mass of each?
Physics
1 answer:
pentagon [3]3 years ago
3 0

Answer:

m₂ = 1.17 kg

Explanation:

Given that,

Force between two objects, F=1.01\times 10^{-8}\ N

Mass of object 1, m_1=5.11\ kg

Distance between masses, r = 19.9 cm = 0.199 m

The gravitational force between two masses is given by :

F=\dfrac{Gm_1m_2}{r^2}

m₂ is the mass of object 2

m_2=\dfrac{Fr^2}{Gm_1}\\\\m_2=\dfrac{1.01\times 10^{-8}\times (0.199)^2}{6.67\times 10^{-11}\times 5.11}\\\\=1.17\ kg

So, the mass of second object is 1.17 kg.

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T = 2 \pi \sqrt{\frac{m}{k} } \\3.5 = 2 (3.14) \sqrt{\frac{5.5}{k} } \\3.5 = 6.28 \sqrt{\frac{5.5}{k} } \\\frac{3.5}{6.28} =  \sqrt{\frac{5.5}{k} } \\0.557 = \sqrt{\frac{5.5}{k} } \\square \ both \ sides\\0.557^2 = (\sqrt{\frac{5.5}{k} })^2 \\0.3106 = \frac{5,5}{k}\\k = \frac{5.5}{0.3106}\\k =  17.71N/m

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