Question

if 2 spheres of equal masses with their centres 0.2m apart attract each other with a force of 1×10^4kg wt. what should be the value of their masses

Answer 1

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Answer 2

Let the mass of each sphere is m

given, separation between them, r = 0.2m

force acting on each of them, F = 1 × 10⁴ kgwt = 10⁴ × 10 N = 10^5 N

[ note : 1kg = 10 N , if we assume g = 10m/s² ]

use gravitational law,

$F=\frac{Gm_1m_2}{r^2}$

here, $m_1=m_2=m$

now, 10^5 = G × m × m/(0.2)²

or, 10^5 × 0.2 × 0.2 = 6.67 × 10^-11 × m²

or, 10^3 × 4 = 6.67 × 10^-11 × m²

or, m² = 4000/(6.67 × 10^-11) = 5997 × 10^10

or, m = √{5997 × 10^10} = 77.44 × 10^5 Kg

hence, mass of each sphere is 7.744 × 10^6 kg