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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Mock Test - Gravitation and Mechanical Properties of Solid

  • question_answer
    In a cosmic event, suppose a planet heavier than the earth with mass KM (K > 1) and radius K'R (K > 1) passes through a path near the earth (M and R are the mass and radius of earth). At what closest distance from surface of planet, we are in danger of  being thrown into space:

    A)  \[{{\left[ \frac{2KGM}{g} \right]}^{1/2}}-\frac{1}{2}K'R\]

    B)  \[{{\left[ \frac{KGM}{2g} \right]}^{1/2}}-\frac{1}{2}K'R\]

    C)  \[{{\left[ \frac{KGM}{g} \right]}^{1/2}}-\frac{1}{2}K'R\]

    D)  \[{{\left[ \frac{KGM}{g} \right]}^{1/2}}-K'R\]

    Correct Answer: D

    Solution :

    [d] we will be thrown into space, if weight mg is equal to gravitational force duet to the planet. If y is the closest distance. \[\frac{GMm}{{{R}^{2}}}=mg=\frac{G(KM)m}{{{(K'R+y)}^{2}}}\] \[{{(K'R+y)}^{2}}=\frac{KGM}{g}\] \[y={{\left( \frac{KGM}{g} \right)}^{1/2}}-K'R\]


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