A) Both decrease by 4%
B) g decrease by 4% and K decrease by 2%
C) Both decrease by 2%
D) g decrease by 4% and K increase by 4%
Correct Answer: A
Solution :
Acceleration due to gravity is\[g=\frac{GM}{{{R}^{2}}}\] and if L be the angular momentum of the earth, then rotational\[KE=\frac{{{L}^{2}}}{2l}\], where l be the moment of inertia. So, \[l=\frac{2}{5}M{{R}^{2}}\] (for sphere) \[\therefore \] Rotational KE = \[\frac{5{{L}^{2}}}{4M{{R}^{2}}}\] Since, angular momentum remains conserved. So, rotational KE \[(K)\propto \frac{1}{{{R}^{2}}}\] \[\therefore \] Both g and K are\[\propto {{R}^{-2}}\]. \[\therefore \]\[\frac{\Delta g}{g}=\frac{\Delta K}{K}=-2\times \frac{\Delta R}{R}\] \[\therefore \]Both g and K would decrease by\[2\times 2%=4%\]
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