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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
7 years ago

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

? K.E = ½ m x 2gR = mgR
Abhishek Dimri
21 Points
3 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 629 Points
one year 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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