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The escape velocity of a sphere of mass m is given by (G = Universal gravitational constant; Mₑ = Mass of the earth and Rₑ = Radius of the earth)

Asked in NEET 1999 · Escape velocity formula

• (1) √(2GMₑm)/(Rₑ)
• (2) √(2GMₑ)/(Rₑ)
• (3) √(GMₑ)/(Rₑ)
• (4) √(2GMₑ+Rₑ)/(Rₑ)

Step-by-step solution

Why the other options are wrong

• (1) comes from keeps the escaping body's own mass, but m cancels from both sides of the energy equation.
• (3) comes from drops the factor 2; √(GMₑ)/(Rₑ) is the orbital speed, not the escape speed.
• (4) comes from adds a length to an energy-per-mass term, which is dimensionally impossible.

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