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The gravitational force between two identical lead spheres kept at 1 m apart is 0.006673 N. Find their masses. (10, 000 kg each)

Difficulty: Hard

Solution:

Gravitational force = F = 0.006673 N
Gravitational constant = G = $6.673 \times 10^{-11} Nm^{2}kg^{-2}$
Distance between the masses = d = 1m
Mass = $m_{1}$ = $m_{2}$ =?
        
F = G $\frac{(m_{1} m_{2})}{d_{2}}$
F = G $\frac{( m \times m )}{d_{2}}$ $(Let \: m_{1} = m_{2}= m)$
F =$\frac{(m ^{2})}{d_{2}}$  


$m^{2}$ = $\frac{F \times d^{2}}{G}$
$m^{2}$ =$\frac{(0.006673 \times 〖(1) 〗^{2})}{( 6.673 \times 〖(10) 〗^{-11} )}$ =$\frac{(\frac{(6673}{1000000)}}{( 6.673 \times〖(10) 〗^{-11})}$ 
              =$\frac{(6.673 \times〖(10) 〗^{-3})}{( 6.673 \times〖(10) 〗^{-11})}$


$√(m^{2}) = 10^{8}$ 
$m = 10^{4}$ = 10000 kg each
Therefore, mass of each lead sphere is 10000 kg.

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