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J & K CET Medical J & K - CET Medical Solved Paper-2004

  • question_answer
    Two planets of radii in the ratio 2 : 3 are made from the material of density in the ratio 3 : 2. Then, the ratio of acceleration due to gravity\[\frac{{{g}_{1}}}{{{g}_{2}}}\] at the surface of the two planets will be :

    A)  1                                            

    B)  2.25

    C)  4/9                                       

    D)  0.12

    Correct Answer: A

    Solution :

                    The acceleration due to gravity (g) is given by \[g=\frac{GM}{{{R}^{2}}}\] where M is mass, G the gravitational constant and R the radius. Since, planets have a spherical shape                 \[V=\frac{4}{3}\pi {{r}^{3}}\] Also, mass (M)= volume (V)\[\times \]density\[(\rho )\]                 \[g=\frac{G\frac{4}{3}\pi {{R}^{3}}\rho }{{{R}^{2}}}\] \[\Rightarrow \]               \[g=\frac{4G\pi \rho R}{3}\] Given,      \[{{R}_{1}}:{{R}_{2}}=2:3\]                 \[{{\rho }_{1}}:{{\rho }_{2}}=\frac{3}{2}\] \[\therefore \]  \[\frac{{{g}_{1}}}{{{g}_{2}}}=\frac{{{\rho }_{1}}{{R}_{1}}}{{{\rho }_{2}}{{R}_{2}}}=\frac{3}{2}\times \frac{2}{3}=1\]


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