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Consider a planet of mass M and radius R as shown in the figure. A particle is projected from the surface of the planet at an angle $θ$ from the radial direction and with a velocity equal to the orbital velocity of a circular orbit at that point, then choose the INCORRECT statement(s):

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Maximum distance of particle from centre of the planet is $(R + Rcosθ)$

Path of the particle is parabola

Time taken by the particle to return to the surface of planet is $\sqrt{\frac{R^{3}}{GM}}$

Time taken by the particle to reach the surface of planet is equal to $\frac{π}{2} \sqrt{\frac{R^{3}}{GM}}$

answer is B, C, D.

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Detailed Solution

From energy conservation

$- \frac{GMm}{R} + \frac{1}{2} {mv}_{0}^{2} = - \frac{GMm}{r} + \frac{1}{2} {mu}^{2}$
${mv}_{0} Rsinθ = mur$

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