MCQ
If a planet consists of a satellite whose mass and radius were both half that of the earth, the acceleration due to gravity at its surface would be ......... $m/{\sec ^2}$ ($ g$ on earth $= 9.8\, m/sec^2$ )
- A$4.9$
- B$8.9$
- ✓$19.6$
- D$29.4$
✓
Answer
Correct option: C.
$19.6$
c
(c) $g = \frac{{GM}}{{{R^2}}}$ $\therefore$ $g \propto \frac{M}{{{R^2}}}$
(c) $g = \frac{{GM}}{{{R^2}}}$ $\therefore$ $g \propto \frac{M}{{{R^2}}}$
According to problem ${M_p} = \frac{{{M_e}}}{2}$ and ${R_p} = \frac{{{R_e}}}{2}$
$\therefore$ $\frac{{{g_p}}}{{{g_e}}} = \left( {\frac{{{M_p}}}{{{M_e}}}} \right)\;{\left( {\frac{{{R_e}}}{{{R_p}}}} \right)^2} = \left( {\frac{1}{2}} \right)\; \times {(2)^2} = 2$
==> ${g_p} = 2{g_e} = 2 \times 9.8 = 19.6\;m/{s^2}$
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