Statement -1 : A tiny shere of mass m and density `rho` is dropped in a tall jar of glycerine of density `rho_(0)` . When the sphere acquires terminal velocity v, the magnitude of viscous force is `mg(1 - rho_(0)//rho)`.
Statement -2 : Viscous force on the body falling in a medium is `F =6 pi eta r v` , where `eta` is the coeff. of viscosity of medium and r is the radius of body

Options

A. Statement -1 is true , Statement -2 is true , Statement -2 is a correct explanation of Statement -1.
B. Statement -1 is true , Statement -2 is true , Statement -2 is not a correct explanation of Statement -1.
C. Statement -1 is true, Statement -2 is false.
D. Statement -1 is false , Statement -2 is true.

Answer

B

Explanation

When the sphere acquires terminal velocity, then the upward viscous force equals the apparent weight in glycerine. Therefore, the magnitude of viscous force is
`=(4)/(3)pi r^(3) rho - (4)/(3)pi r^(3) rho_(0) = (4)/(3)pi r^(3) (rho - rho_(0))`
`=(mg)/(rho) (rho - rho_(0)) = mg (1 -(rho_(0))/(rho))`
Thus statement - 1 is correct. Here statement - 2 is correct but Reason can not explain properly the Assertion.