- Home
- Standard 11
- Physics
7.Gravitation
normal
On a hypothetical planet satellite can only revolve in quantized energy level i.e. magnitude of energy of a satellite is integer multiple of a fixed energy. If two successive orbit have radius $R$ and $\frac{3R}{2}$ what could be maximum radius of satellite
A
$9R$
B
$6R$
C
$4R$
D
$3R$
Solution
For energy in radius $r_{i}=\left|\frac{-G M m}{2 r}\right|=n k$
where $n$ is integer $k$ is constant energy, now
$\frac{G M m}{2 R}=n k$
$\frac{G M m}{2\left(\frac{3 R}{2}\right)}=(n-1) k$
so solving $\mathrm{k}=\frac{G M m}{6 R}$
now this implies that for $R_{\max }$
$\frac{G M m}{2 R_{\max }}=(1) \frac{G M m}{6 R} \Rightarrow R_{\max }=3 R$
Standard 11
Physics
