A) \[{{\left( \frac{\sigma -1}{\sigma } \right)}^{1/3}}\]
B) \[{{\left( \frac{\sigma }{\sigma -1} \right)}^{1/3}}\]
C) \[{{\left( \frac{\sigma +1}{\sigma } \right)}^{2}}\]
D) \[{{\left( \frac{\sigma }{\sigma +1} \right)}^{3}}\]
Correct Answer: B
Solution :
Weight of the hollow sphere \[=\frac{4}{3}\pi ({{R}^{3}}-{{r}^{3}})\sigma g=\frac{4}{3}\pi R_{1}^{3}g\] Weight of water displaced \[=\frac{4}{3}\pi {{R}^{3}}\times l\times g\] Now according to law of floatation \[\frac{4}{3}\pi ({{R}^{3}}-{{r}^{3}})\sigma g=\frac{4}{3}\pi R_{1}^{3}g\] \[\frac{R}{r}={{\left( \frac{\sigma }{\sigma -1} \right)}^{1/3}}\]You need to login to perform this action.
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