SATHEE: Gravitation Question 125

Gravitation Question 125

Question: The masses and radii of the earth and moon are $[M_{1},, R_{1}]$ and $[M_{2},, R_{2}]$ respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is [MP PET 1997]

Options:

A) $[2 \sqrt{\frac{G}{d} (M_{1} + M_{2})}]$

B) $[2 \sqrt{\frac{2 G}{d} (M_{1} + M_{2})}]$

C) $[2 \sqrt{\frac{G m}{d} (M_{1} + M_{2})}]$

D) $[2 \sqrt{\frac{G m (M_{1} + M_{2})}{d (R_{1} + R_{2})}}]$

Show Answer

Answer:

Correct Answer: A

Solution:

Gravitational potential at mid point $[V = \frac{- G M_{1}}{d / 2} + \frac{- G M_{2}}{d / 2}]$ Now, $[P E = m \times V = \frac{- 2 G m}{d} (M_{1} + M_{2})]$ [m = mass of particle] So, for projecting particle from mid point to infinity $[K E, =, |, P E, |]$ $[\Rightarrow, \frac{1}{2} m v^{2} = \frac{2, G m}{d} (M_{1} + M_{2})]$ $[\Rightarrow, v = 2 \sqrt{\frac{G, (M_{1} + M_{2})}{d}}]$

Gravitation Question 125

Options:

Answer:

Solution:

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Gravitation Question 125

Question: The masses and radii of the earth and moon are [M1,,R1] and [M2,,R2] respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is [MP PET 1997]

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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