A) 29.4 m/s2
B) 19.6 m/s2
C) 9.8 m/s2
D) 4.9 m/s2
Correct Answer: B
Solution :
From law of gravitation, the force of attraction acting on a body due to earth is \[F=\frac{G{{M}_{e}}m}{R_{e}^{2}}\] ?(i) Also acceleration due to gravity g arises due to force F. From Newton's second law \[F=mg\] Equating Eqs. (i) and (ii), we get \[mg=G\frac{{{M}_{e}}m}{R_{e}^{2}}\] \[\Rightarrow \] \[g=\frac{G{{M}_{e}}}{R_{e}^{2}}\] ?(iii) Here, \[{{M}_{p}}=\frac{{{M}_{e}}}{2},{{R}_{p}}=\frac{{{R}_{e}}}{2}\] \[\therefore \] \[{{g}_{p}}=\frac{G{{M}_{e}}/2}{{{({{R}_{e}}2)}^{2}}}\] Dividing Eqs. (iv) by (iii) , we have \[\frac{{{g}_{p}}}{g}=\frac{2G{{M}_{e}}}{R_{e}^{2}}\times \frac{R_{e}^{2}}{G{{M}_{e}}}\] \[{{g}_{p}}=2g\] \[{{g}_{p}}=2\times 9.8=19.6\,m/{{s}^{2}}\]
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