NEET Sample Paper NEET Sample Test Paper-9

  • question_answer A sphere of radius R has a concentric cavity of radius r. The relative density of the material of the sphere is a. It just floats when placed in a tank full of water. The ratio \[\frac{R}{r}\] is:

    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 \[\frac{4}{3}\pi ({{R}^{3}}-{{r}^{3}})\sigma g=\frac{4}{3}\pi R_{1}^{3}g\]                 \[\frac{R}{r}={{\left( \frac{\sigma }{\sigma -1} \right)}^{1/3}}\]


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