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The ratio of the masses of two planets is 2:3 and the ratio of their radii is 4:7. What is the ratio of their accelerations due to gravity?
A8 : 21
B49 : 48
C2 : 3
D16 : 49
Answer & Solution
Correct answer: B. 49 : 48
1. Acceleration due to gravity g = GM / R², so g is proportional to M / R².
2. For planet 1: M₁/R₁² = 2 / 4² = 2/16. For planet 2: M₂/R₂² = 3 / 7² = 3/49.
3. Ratio g₁ : g₂ = (2/16) : (3/49) = (2 x 49) : (3 x 16) = 98 : 48 = 49 : 48.
4. Rule out 2:3: that uses only the mass ratio and ignores the radii.
5. Rule out 8:21: that wrongly multiplies M by R instead of dividing by R².
_Source: Samacheer Kalvi (TN SCERT) Class 10 Science, Unit 1 "Laws of Motion", p.21_
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