Question

Two stones are projected with the same speed but making different angles with horizontal. Their ranges are equal. If the ranges of projection of one is $\pi /3$ and its maximum height is $h_1$ then the maximum height of the other will be

• A. $\frac{Rg}{{\omega }^2}$
• B. $\frac{R^{2}g}{{\omega }^{}}$
• C. $\frac{R^{2}g}{{\omega }^2}$
• D. $\frac{R^2\omega }{g^{}}$

Answer 1

The correct option is C $\frac{R^{2}g}{{\omega }^2}$

Assuming this to be a geo-stationary satellite, the angular speed of the satellite is the same as the angular speed of rotation of the earth.

Hence, we have:
$GMm/r^2=m{w}^{2}r$ and $GM/R^2=g$
Hence, $r^3=R^{2}g/w^2$