Question

The ratio of $KE$ of a planet at the points 1 and 2 is

• A. $\left(\frac{ r _{1}}{ r _{2}}\right)^{2}$
• B. $\left(\frac{ r _{2}}{ r _{1}}\right)^{2}$
• C. $\frac{r_{1}}{r_{2}}$
• D. $\frac{ r _{2}}{ r _{1}}$

Answer 1

Answer: (B)

$v_{1} r _{1}=v_{2} r _{2}$
$\Rightarrow \frac{v_{1}}{v_{2}}=\frac{r_{2}}{r_{1}}$
So, $\frac{K_{1}}{K_{2}}=\left(\frac{v_{1}}{v_{2}}\right)^{2}$
$=\frac{r_{2}^{2}}{r_{1}^{2}}$