GAT PYQ 2024 Mock Test – I – Q6

A spherical shell of outer radius R and inner
radius R/2 contains a solid sphere of radius
R/2 (see figure). The density of the material of
the solid sphere is r and that of the shell is r/2.
What is the average mass density of the larger
sphere thus formed?

• 3r/4
• 9r/16
• 7r/8
• 5r/8

Average density = Total mass / Total volume
= (p1*V1 + p2*V2)/V
= (p * (4/3)*pi*(R/2)^3 + (p/2) * ( (4/3)*pi*R^3 – (4/3)*pi*(R/2)^3 ) ) / ( (4/3)*pi*R^3 )
= (p * (1/8) + (p/2) * (1 – 1/8)) = p/8 + (p/2)*(7/8) = p/8 + 7p/16 = 9p/16.