- The acceleration due to gravity on the surface of a planet is given by g = GM/R², where G is the gravitational constant, M is the mass, and R is the radius. - The mass (M) remains the same. - The radius is shrunk by one per cent, so the new radius R' = R - 0.01R = 0.99R. - The new acceleration due to gravity g' = GM/(R')² = GM/(0.99R)² = GM/ The change in g is g' - g ≈ 1.0199g - g = 0.0199g. - The percentage change is (change / original) 100 = (0.0199g / g) 100 = 1.99%. - This is approximately a 2% increase.
If the radius of the earth were shrunk by one per cent, its mass remaining the same, the value of ‘g’ on the earth’s surface would
Asked in UPPCS Prelims 2003 · Topic: Mechanics (Gravitation and Central Force Motion (Kepler's Laws))
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