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Grade: 11
        
Q. A body is projected upward from the Earth surface. It's velocity is half of the escape velocity. Find the total energy of it on the surface. If the maximum distance reached bu the body from earth - centre br r, find r.
11 months ago

Answers : (1)

Arun
22576 Points
							
We know that the escape velocity of Earth = Ve = √[2gR]
       g = gravity due to Earth
      1/2 m (Ve)² - G Mm/R = 0   for the object to escape from Earth.
       (or,  KE + PE = 0)
When the body is projected from Earth's surface:
     Given  u = initial velocity = Ve /2 = √(gR/2)
     Initial  KE = 1/2 m u² = m g R/4 = G M m /(4R)
     Initial  PE = - GMm/R
     Total initial energy = - 3 GMm /(4R)
 When the body reaches a height h above surface of Earth and stops:
     v = 0. Final KE = 0.
     Final PE = - G M m/ (R+h)
From conservation of Energy:
           - GMm/(R+h) = - 3Gm/ (4R)
            3 (R+h) = 4 R
              h = R/3
11 months ago
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