A body is projected vertically upwards from the surface of the earth with a velocity sufficient to carry it to infinity. The time taken by it to each height h is

Q: A body is projected vertically upwards from the surface of the earth with a velocity sufficient to carry it to infinity. The time taken by it to each height h is (Given, R = radius of the earth)

(a) $\frac{1}{3} \sqrt{\frac{2R}{g}}[(1 + \frac{h}{R})^{3/2}- 1]$

(b) $ \sqrt{\frac{R}{g}}[(1 + \frac{h}{R})^{3/2}- 1]$

(c) $\frac{1}{2} \sqrt{\frac{R}{g}}[(1 +\frac{h}{R})^{3/2}- 1]$

(d) $\frac{1}{3} \sqrt{\frac{2R}{g}}[(1 + \frac{h}{R})^{3/2}- 1]$

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Ans: (a)