If the terminal speed of a sphere of gold (density =`19.5kgm^(-3))` density of liquid `=1.5kgm^(-3))` is `0.2ms^(-1)` in a viscous liquid . What is the terminal speed of a sphere of silver (density `=10.5kgm^(-3))` of the same size in the same liquid ?

Options

A. `0.2ms^(-1)`
B. `0.4ms^(-1)`
C. `0.133ms^(-1)`
D. `0.1ms^(-1)`

Answer

d

Explanation

Terminal velocity `v_(t)=(2)/(9)(r^(2)g)/(n)(rho-rho_(o))`
(Here , `(2)/(9)*(r^(2)g)/(n)` is constant)
`thereforev_(t)prop(rho-rho_(o))`
`therefore((v_(t))g)/((v_(t))_(s))=(rho_(g)-rho_(o))/(rho_(s)-rho_(o))=(19.5-1.5)/(10.5-1.5)=(18)/(9)=2`
`therefore(v_(t))_(s)=((v_(t))g)/(2)=(0.2)/(2)=0.1ms^(-1)`