Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

<p>The escape velocity ($v_{\text{esc}}$) for a planet with mass $M$ and radius $R$ is given by the formula:</p> <p>$v_{\text{esc}} = \sqrt{\frac{2GM}{R}}$</p> <p>where $G$ is the gravitational constant.</p> <p>For Earth, let's denote its mass as $M_E$ and its radius as $R_E$. The escape velocity is given as 11.2 km/s. Therefore:</p> <p>$v_{\text{esc, Earth}} = \sqrt{\frac{2G M_E}{R_E}} = 11.2 \text{ km/s}$</p> <p>For the planet in question, its mass $M_P$ is $M_E/8$ and its radius $R_P$ is $R_E/2$. The escape velocity from the planet is:</p> <p>$$ v_{\text{esc, Planet}} = \sqrt{\frac{2G M_P}{R_P}} = \sqrt{\frac{2G (M_E/8)}{R_E/2}} $$</p> <p>Simplifying the expression:</p> <p>$$ v_{\text{esc, Planet}} = \sqrt{\frac{2G (M_E/8)}{R_E/2}} = \sqrt{\frac{2G M_E \cdot 2}{8R_E}} = \sqrt{\frac{G M_E}{2R_E}} $$</p> <p>Now, relate it to the escape velocity from Earth:</p> <p>$v_{\text{esc, Planet}} = \frac{1}{\sqrt{4}} \cdot v_{\text{esc, Earth}}$</p> <p>Calculating further:</p> <p>$v_{\text{esc, Planet}} = \frac{1}{2} \cdot 11.2 \text{ km/s} = 5.6 \text{ km/s}$</p> <p>Thus, the escape velocity from the planet is 5.6 km/s. </p> <p><strong>Option C: 5.6 km/s</strong> is the correct answer.</p>