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A particle of mass m is thrown upwards from the surface of the earth, with a velocity u. The mass and the radius of the earth are, respectively, M and R. G is gravitational constant and g is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is

Asked in NEET 2011 · Escape velocity formula

• (1) √(2GM)/(R²)
• (2) √(2GM)/R
• (3) √(2gM)/(R²)
• (4) √2gR²

Step-by-step solution

Why the other options are wrong

• (1) comes from uses R² in the denominator, which makes the expression an acceleration times a length, not a squared speed.
• (3) comes from replaces G by g, which is dimensionally inconsistent.
• (4) √2gR² has units of length per time times length; the escape speed is √2gR.

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