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MHT CET 2021 (24 Sep, Shift 2) · Acceleration Due to Gravity

Acceleration Due to Gravity question from MHT CET 2021 (24 Sep, Shift 2)

Q91MHT CET 2021 · 24 SEP · SHIFT 2Medium

Acceleration Due to Gravity

The length of the seconds pendulum is lm on earth. If the mass and diameter of the planet is 1.5 times that of the earth, the length of the seconds pendulum on the planet will be nearly

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Answer: (a)

  1. gp=G(1.5M)(1.5R)2=g1.5g_p = \frac{G(1.5M)}{(1.5R)^2} = \frac{g}{1.5}
  2. For a fixed period T=2πlgT = 2\pi\sqrt{\frac{l}{g}}, l∝gl \propto g.
  3. lp=11.5×1 m≈0.67 ml_p = \frac{1}{1.5}\times 1\text{ m} \approx 0.67\text{ m}
  4. So the answer is (a) 0.67 m0.67\text{ m}.
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