Two solid spheres of same metal but of mass M and 8M fall simultaneously on a viscous liquid and their terminal
Two solid spheres of same metal but of mass M and 8M fall simultaneously on a viscous liquid and their terminal velocities are v and nv, then value of n is
A) 16
B) 8
C) 4
D) 2
8 views
1 Answers
The terminal velocity is given by v, where v α r2 (r = radius of the sphere). The mass of the sphere can be given by
\( m = \frac{4}{2} \pi r^3\rho, thus\,m \propto r^3 \)
\(\frac{m_1}{m_2} = \frac{1}{8}=( \frac{r_1}{r_2})^3 \,\,\Rightarrow\frac{r_1}{r_2} = \frac{1}{2}\)
\( and \, since, \frac{v_1}{v_2} = (\frac{r_1}{r_2})^2 = \frac{1}{4}\)
\( \Rightarrow\frac{v}{nv} = \frac{1}{4}\)
\( \Rightarrow n=4\)
8 views
Answered