Q. 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
A) √(2gR²)
B) √(2GM/R²)
C) √(2GM/R)
D) √(2gM/R²)
Explanation
[Solution from source] To not return, the particle must reach infinity: ½mu² = GMm/R, so u = √(2GM/R) (= √(2gR)). √(2GM/R²) and √(2gR²) are dimensionally wrong as speeds. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.