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A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is
  • a)
    R/3
  • b)
    R/2
  • c)
    R/4
  • d)
    R/5
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A body is projected vertically upwards from the surface of a planet of...
Energy conservation ,

-GmM/R. +. 0.5×m×0.25×2GM/R. =.

-GMm/(R+H)

SOLVE THIS U GET "R/3". AS UR ANSWER
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Community Answer
A body is projected vertically upwards from the surface of a planet of...
Solution:

Given,

Initial velocity of the body, u = 1/2 × escape velocity

We know that escape velocity, v = √(2GM/R)

where G is the universal gravitational constant, M is the mass of the planet and R is the radius of the planet.

Let's assume the maximum height attained by the body from the surface of the planet is h.

At the maximum height, the final velocity of the body will be zero.

Using the equation of motion, v²=u²+2gh, we can find the maximum height.

0 = (1/2 × escape velocity)² + 2gh

h = (1/8) × (2GM/R) × (R/(2GM/R))²

h = R/3

Therefore, the maximum height attained by the body is R/3.

Hence, the correct answer is option A, i.e., R/3.
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A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body isa)R/3b)R/2c)R/4d)R/5Correct answer is option 'A'. Can you explain this answer?
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