Assertion (A): If both the mass and radius of the earth decreases by 1%,
the value of acceleration due to gravity will increase by 2%.
Reason (R): g= GMm/R2
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Explanation:
The acceleration due to gravity is: g=
R
2
GM
The new value of g would be: g
′
=
(0.99R)
2
G(0.99M)
≃1.01
R
2
GM
=1.01g
Thus,g would increase by about 1%.The new escape velocity would be:
V
e
′
=
0.99R
2×0.99M×G
=
R
2MG
=V
e
Thus,the escape velocity will remain unchanged.The potential energy of a body of mass m on earth's surface would be
−
(0.99R)
GM(0.99M)
=−
R
GmM
Thus,the potential energy will also remain unchanged.Hence,the correct choices are (b) and (d).
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