Two solid spheres of same metal but of mass M and 8M fall simultaneous

1.	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
Answer» 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 \( m = \frac{4}{2} \pi r^3\rho, thus\,m \propto r^3\) \(\frac{m_1}{m_2} = \frac{1}{8}=( \frac{r_1}{r_2})^3 \,\,\Rightarrow\frac{r_1}{r_2} = \frac{1}{2}\) \( and \, since, \frac{v_1}{v_2} = (\frac{r_1}{r_2})^2 = \frac{1}{4}\) \( \Rightarrow\frac{v}{nv} = \frac{1}{4}\) \( \Rightarrow n=4\)

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

Answer»

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

\( m = \frac{4}{2} \pi r^3\rho, thus\,m \propto r^3\)

\(\frac{m_1}{m_2} = \frac{1}{8}=( \frac{r_1}{r_2})^3 \,\,\Rightarrow\frac{r_1}{r_2} = \frac{1}{2}\)

\( and \, since, \frac{v_1}{v_2} = (\frac{r_1}{r_2})^2 = \frac{1}{4}\)

\( \Rightarrow\frac{v}{nv} = \frac{1}{4}\)

\( \Rightarrow n=4\)