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The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is (a) mgR/2 (b) 2 mg /R (c) mgR (d) mgR/4

The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is
(a) mgR/2
(b) 2 mg /R
(c) mgR
(d) mgR/4

Grade:6

3 Answers

Deepak Patra
askIITians Faculty 471 Points
9 years ago

(c) K.E. = ½ mv2e ­where ve = escape velocity = v2gR

? K.E = ½ m x 2gR = mgR
Abhishek Dimri
21 Points
6 years ago
The answer is (c)We know that K.E. 1/2 mV^2e. ..........(1)Where Ve = escape velocityVe = √(2gR)V^2e = 2gRPutting the value of V^2e in eqn (1) we have K.E. = 1/2 m2gRK.E. = mgR
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the answer to your question.
 
Since only conservative force(Gravitational force acts), net mechanical energy is conserved.
Hence, Ki + Ui = Kf + Uf
Hence, Ki + ( – GMm/R) = 0 + 0
Hence, Ki = GMm/R = GM/R x m = GM/R2 x m x R = mgR
 
Hope it helps,
Thanks and regards,
Kushagra

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