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9th Class Science Gravitation and Floatation Question Bank Gravitation

  • question_answer
    A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum distances of the planet from the sun are \[{{r}_{1}}\] and \[{{r}_{2}}\]. respectively. The time period of the planet is proportional to

    A)  \[{{r}_{1}}^{\frac{3}{2}}\]                           

    B)         \[{{r}_{2}}^{\frac{3}{2}}\]

    C)  \[\frac{{{({{r}_{1}}+{{r}_{2}})}^{\frac{3}{2}}}}{2}\]             

    D)         \[\frac{{{({{r}_{1}}-{{r}_{2}})}^{\frac{3}{2}}}}{2}\]

    Correct Answer: C

    Solution :

     According to Kepler's law,                 \[{{T}^{2}}\propto {{a}^{3}}\] Here, \[a=\]semi-major axis\[=\left( \frac{{{r}_{1}}+{{r}_{2}}}{2} \right)\] \[\therefore \]  \[{{T}^{2}}\propto {{\left( \frac{{{r}_{1}}+{{r}_{2}}}{2} \right)}^{3}}\] \[\Rightarrow \]               \[T\propto {{\left( \frac{{{r}_{1}}+{{r}_{2}}}{2} \right)}^{3/2}}\]


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