Sample 1Medium
A graph shows the acceleration due to gravity g on the y-axis against distance r from the Earth's centre on the x-axis. It rises in a straight line from zero at r = 0 to g at r = R (the Earth's surface), then falls as 1/r² beyond R. Point P is at r = R/2 and point Q at r = 2R. What is the ratio of the acceleration due to gravity at P to that at Q?
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The answer is A.
Inside the Earth g varies as r, so at R/2 it is g/2. Outside it varies as 1/r², so at 2R it is g/4. The ratio is (g/2) : (g/4) = 2 : 1.
- B.
1 : 2 inverts the correct ratio.
- C.
1 : 1 would need equal values; g/2 and g/4 are not equal.
- D.
4 : 1 treats g at P as equal to the surface value g.
NCERT: Class 11 Physics, Chapter 7