Newton's Law Of Universal Gravitation

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Two lead spheres each of mass 8 kg are placed so their centres are 20 cm apart on a smooth bench. What is the gravitational force of attraction between them?

RankGuru · Accepted Answer

According to NCERT Class 11, Chapter 8 (Gravitation), every point mass attracts every other point mass with a force directed along the line joining their centres, given by Newton's law of gravitation $F = \dfrac{G m_1 m_2}{r^2}$, where $G = 6.67 	imes 10^{-11}\,	ext{N m}^2	ext{kg}^{-2}$ is the universal gravitational constant. This law is universal, applying equally to laboratory spheres and to planets. Because each sphere is uniform, the shell theorem lets us treat all of its mass as concentrated at its centre, so the centre-to-centre distance $r = 0.20\,	ext{m}$ is the correct separation to use. Substituting $m_1 = m_2 = 8\,	ext{kg}$ gives $F = \dfrac{(6.67 	imes 10^{-11})(8)(8)}{(0.20)^2} = \dfrac{6.67 	imes 10^{-11} 	imes 64}{0.04} = 1.07 	imes 10^{-7}\,	ext{N}$. The option $2.13 	imes 10^{-7}\,	ext{N}$ doubles the result, an error from mishandling the product of the masses. The value $1.07 	imes 10^{-5}\,	ext{N}$ wrongly keeps $r$ in centimetres rather than converting to metres. The value $4.27 	imes 10^{-9}\,	ext{N}$ comes from using $r = 2\,	ext{m}$ instead of $0.20\,	ext{m}$. As a plausibility check, gravitational forces between everyday masses are extremely small because $G$ is tiny, so a result of order $10^{-7}\,	ext{N}$ is entirely consistent.

Newton's Law Of Universal Gravitation

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