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JEE Main 2013 (22 Apr, Shift 1) · Newton's Law of Gravitation

Newton's Law of Gravitation question from JEE Main 2013 (22 Apr, Shift 1)

Q20JEE Main 2013 · 22 APR · SHIFT 1Difficult

Newton's Law of Gravitation

The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon = 7.36×10227.36 \times 10^{22} kg, radius of the moon's orbit = 3.8×1083.8 \times 10^{8} m).

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Answer: (a)

  1. Moon's pull gives the earth an acceleration a=GMmr2a = \frac{GM_m}{r^2}, toward the sun at eclipse and away from it on the other side.
  2. a=6.67×10−11×7.36×1022(3.8×108)2≈3.4×10−5a = \frac{6.67 \times 10^{-11} \times 7.36 \times 10^{22}}{(3.8 \times 10^{8})^2} \approx 3.4 \times 10^{-5} m/s2^2
  3. Change =2a≈6.7×10−5= 2a \approx 6.7 \times 10^{-5} m/s2^2
  4. So the answer is (a) 6.73×10−56.73 \times 10^{-5} m/s2^2.
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