If the diameter of the earth becomes two times its present value and its mass remains unchanged, then how would the weight of an object on the surface of the earth be affected?
Correct answer: B. Becomes one fourth
- A. Becomes double
- B. Becomes one fourth
- C. Becomes one third
- D. Remains same
- E. Becomes half
Explanation
Let M be the mass of earth and R be the radius, we know, g=GM/R2 so, if diameter is doubled i.e. d' = 2d which means R' = d = 2R ⇒ g' = GM/4R2 = g/4 So g becomes g/4. Also Weight=Mass of the object W'=(mass of object*g)/4 That is, the weight becomes 1/4.
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