Assuming V as the gravitational potential at the centre of earth, the potential at a distance half the radius from its centre will be 11V/(10+x). The value of x is
Physics · Mixed Chapter
JEE Mains

Question

Assuming V as the gravitational potential at the centre of earth, the potential at a distance half the radius from its centre will be 11V/(10+x). The value of x is

G1 Physics · Accepted Answer

Step 1: For a uniform solid Earth, V(r)=−(GM/2R)[3−(r²/R²)] for r≤R. Step 2: At the centre V(0)=−3GM/(2R)=V. At r=R/2, V(R/2)=−(GM/2R)(3−1/4)=−11GM/(8R). Step 3: Ratio V(R/2)/V(0)=[11/8]/[3/2]=11/12. Step 4: Given 11V/(10+x)=(11/12)V, so 10+x=12 and x=2.