Newton's Law of Gravitation: Practice Problem & Solution
The earth (mass $= 6 \times 10^{24}\text{ kg}$) revolves around the sun with an angular velocity of $2 \times 10^{-7}\text{ rad/s}$ in a circular orbit of radius $1.5 \times 10^8\text{ km}$. The force exerted by the sun on the earth, in newton, is: (1995)
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Newton's Law of Gravitation. Understanding the underlying formula is key to arriving at the correct answer below:
The force is the centripetal force $F = mR\omega^2$. Substituting the values: $F = (6 \times 10^{24}) \times (1.5 \times 10^{11}\text{ m}) \times (2 \times 10^{-7})^2 = 9 \times 10^{35} \times 4 \times 10^{-14} = 36 \times 10^{21}\text{ N}$.
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