JEE Mains · Physics · STD 11 - 7. gravitation
A body of mass \(m\) is projected with velocity \(\lambda v_{e}\) in vertically upward direction from the surface of the earth into space. It is given that \(v _{ e }\) is escape velocity and \(\lambda<1\). If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be. ( \(R\) : radius of earth)
- A \(\frac{R}{1+\lambda^{2}}\)
- B \(\frac{R}{1-\lambda^{2}}\)
- C \(\frac{R}{1-\lambda}\)
- D \(\frac{\lambda^{2} R}{1-\lambda^{2}}\)
Answer & Solution
Correct Answer
(B) \(\frac{R}{1-\lambda^{2}}\)
Step-by-step Solution
Detailed explanation
\(-\frac{ GMm }{ R }+\frac{1}{2} m \lambda^{2} V _{ e }^{2}=-\frac{ GMm }{ h }\) \(-\frac{ GMm }{ R }+\frac{1}{2} \lambda^{2} \frac{2 GMm }{ R }=-\frac{ GMm }{ h }\) \(\frac{\lambda^{2}}{ R }-\frac{1}{ R }=\frac{-1}{ h }\) \(\frac{1}{ h }=\frac{1-\lambda^{2}}{ R }\)…
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