Universal Law Of Gravitation

Question

Two lead spheres of masses 3 kg and 12 kg are placed with their centres 0.5 m apart on a laboratory bench. What is the gravitational force of attraction between them? (G = 6.67 × 10^-11 N·m^2/kg^2)

RankGuru · Accepted Answer

Newton's universal law of gravitation states that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres, written as $F = G\frac{m_1 m_2}{r^2}$. For uniform spheres the entire mass acts as if concentrated at the centre, so the centre-to-centre distance is used directly. Substituting $m_1 = 3$ kg, $m_2 = 12$ kg and $r = 0.5$ m gives $F = \frac{6.67	imes10^{-11}	imes 3 	imes 12}{(0.5)^2} = \frac{6.67	imes10^{-11}	imes 36}{0.25} = 9.60	imes10^{-9}$ N. The option $4.80	imes10^{-9}$ N is wrong because it omits squaring the distance and divides by $0.5$ instead of $0.25$. The value $2.40	imes10^{-9}$ N is wrong as it uses an incorrect mass product. The value $1.92	imes10^{-8}$ N is wrong because it doubles the force without justification. This is the standard NCERT inverse-square treatment. A plausibility check confirms the force is extremely tiny, as expected for ordinary laboratory masses.

Universal Law Of Gravitation

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