A) (I) and (Ill)
B) (i) and (iv)
C) (ii) and (iv)
D) (Ill) and (iv)
Correct Answer: C
Solution :
If both the mass and radius of the earth decrease by 1%, the value of acceleration due to gravity \[g=\frac{G(0.99{{M}_{e}})}{{{(0.99{{R}_{e}})}^{2}}}\approx 1.01\frac{G{{M}_{e}}}{R_{e}^{2}}=1.01g\] So, g would increase by \[(1.01-1)\times 100%=1%\] New escape velocity would be \[{{\upsilon }_{e}}=\sqrt{\frac{2\times 0.99\,{{M}_{e}}G}{0.99{{R}_{e}}}}=\sqrt{\frac{2G{{M}_{e}}}{{{R}_{e}}}}={{\upsilon }_{e}}\] So, it will remain unchanged. Also gravitational potential energy \[=-\frac{Gm(0.99{{M}_{e}})}{0.99{{R}_{e}}}=-\frac{G{{M}_{e}}m}{{{R}_{e}}}\] Hence, it also will remain same.
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