The radius of the earth is reduced by 4%. The mass of the earth remains unchanged. The escape velocity increases by K%. Find the value of K.

Escape velocity =v=2GMR ⇒ v2=2GMR......(i) v2=(2GM)R−1  Differentiating both sides, we get,  2vdvdR=−2GMR2⇒vdvdR=GMR2.......(ii)  Dividing (ii) by (i), 1vdvdR=−12R ⇒dvv×100=12×4%=2% ∴  If the radius decreases by 4% , escape velocity will increase by 2%.