Universal Law Of Gravitation

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 $F=\frac{6.67\times 10^{-11}\times 3\times 12}{(0.5{)}^2}=\frac{6.67\times 10^{-11}\times 36}{0.25}=9.60\times 10^{-9}$ N. The option $4.80\times 10^{-9}$ N is wrong because it omits squaring the distance and divides by $0.5$ instead of $0.25$. The value $2.40\times 10^{-9}$ N is wrong as it uses an incorrect mass product. The value $1.92\times 10^{-8}$ 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.