Gravitation — Physics STD 11 Science — Question

1. The minimum speed required for an object to reach infinity (i.e., to get escape from earth gravitational pull) is called escape velocity.
2. $\frac{1}{2}\text{m}\Big(\text{v}_{\text{i}}^2\Big)_{\text{e}}=\frac{\text{GmM}_{\text{p}}}{\text{h}+\text{R}_{\text{p}}}$

$\begin{bmatrix}\text{where M}_{\text{p}}=\text{Mass of planet}\\\ \ \ \ \ \ \ \ \ \ \text{R}_{\text{p}}=\text{Radius of planet}\end{bmatrix}$

If the object is thrown from surface of a planet h = 0, we get

$(\text{v}_{\text{i}})_{\text{e}}=\sqrt{\frac{2\text{GM}_{\text{p}}}{\text{R}_{\text{p}}}}$

$\text{but }\text{g}=\frac{\text{GM}_{\text{p}}}{\text{R}_{\text{p}}}\text{ we get}$

$(\text{v}_{\text{i}})_{\text{e}}=\sqrt{2\text{gR}_{\text{p}}}$

3. Depends on location as 'g' varies with location, as most of the celestial bodies are not perfectly spherical.