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NEET 2024
Exam
NEET
Year
2024
Subject
Physics
Chapter
Gravitation

NEET 2024 · Physics · Gravitation

The escape velocity for earth is v . A planet having 9 times mass...

The escape velocity for earth is vv. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

Options

  1. Av3\frac{v}{3}
  2. B2v3\frac{2 v}{3}
  3. C3v4\frac{3 v}{4}
  4. D9v4\frac{9 v}{4}

Correct answer

C. 3v4\frac{3 v}{4}

Step-by-step solution

Escape velopity of object from planet is given by (ve)p=2GMpRp∴(ve)p∝MpRp\left(v_e\right)_p=\sqrt{\frac{2 G M_p}{R_p}} \therefore \quad\left(v_e\right)_p \propto \sqrt{\frac{M_p}{R_p}} Now, Mp=9MeandRp=16ReM_p=9 M_e and R_p=16 R_e (given) (ve)p(ve)e=MpRp×ReMe=9Me16Re×ReMe=916=34⇒(ve)p=34v\frac{\left(v_e\right)_p}{\left(v_e\right)_e}=\sqrt{\frac{M_p}{R_p} \times \frac{R_e}{M_e}}=\sqrt{\frac{9 M_e}{16 R_e} \times \frac{R_e}{M_e}}=\sqrt{\frac{9}{16}}=\frac{3}{4} \Rightarrow \quad\left(v_e\right)_p=\frac{3}{4} v
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