Correct Answer - A
Let `rho` the density of the material `rho_(0)` be the density of water. When the sphere has just started sinking the weight of the sphere`=` weight of water displaced (approx)
`implies(4)/(3)pi(R^(3)-r^(3))rhog=(4)/(3)piR^(3)rho_(0)g`
`implies(R^(3)-r^(3))rho=R^(3)rho_(0)implies((R^(3)-r^(3)))/(R^(3))=(rho_(0))/(rho)`
`implies(r)/(R)=((7)^(1//3))/(2)`