A) 16
B) 8
C) 4
D) 2
Correct Answer: C
Solution :
The terminal velocity is given by v, where \[v\propto {{r}^{2}}\] (r = radius of the sphere). The mass of the sphere can be given by \[m=\frac{4}{3}\pi {{r}^{3}}\rho ,\]thus \[m\propto {{r}^{3}}.\] So, according to the question, \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{1}{8}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}\] \[\Rightarrow \] \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{1}{2}\] and since, \[\frac{{{v}_{1}}}{{{v}_{2}}}=\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)={{\left( \frac{1}{2} \right)}^{2}}=\frac{1}{4}\] \[\Rightarrow \] \[\frac{v}{mv}=\frac{1}{v}\Rightarrow n=4\]
You need to login to perform this action.
You will be redirected in
3 sec
