A uniform sphere of mass 64kg and radius 4m , a concentric cavity of radius 1m is made. The gravitational force on a mass of 1kg at a distance of 2m from the center of the spheres is (take G=6.67×10−11Nm2/kg2 )
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a
4×10−11N
b
11.7×10−11N
c
6.67×10−11N
d
9.3×10−11N
answer is B.
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Detailed Solution
Enet=Field at an interior point of solid sphere. Field at an exterior point of cavity.mass of given sphere=M=64kg; mass of cavity=M1; univform density=ρM1M=43π13×ρ43π43×ρM1=M64=1kg=mass of cavity---(1)gravitational field strength=Enet =Esolid sphere interior point −Ecavity Esolid =GMrR3Ecavity =GM1r2Enet =G(64)243−G×(1)22Enet =2G−G4=7G4Enet =11.67×10−11N/kgEnet=11.7×10−11N/kg∴ Gravitational force is F=m×Enet=1×11.7×10−11=11.7×10−11N