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JEE Main & Advanced Physics Two Dimensional Motion Question Bank Self Evaluation Test - Motion in a Plane

  • question_answer
    A projectile is fired from the surface of the earth with a velocity of 5 \[m{{s}^{-1}}\,\] and angle \[\theta \] with the horizontal. Another projectile fired from another planet with a velocity of 3 \[m{{s}^{-1}}\,\]at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in \[\text{m}{{\text{s}}^{-2}}\]) given \[\text{g = 9}\text{.8 m/}{{\text{s}}^{\text{2}}}\]

    A) 3.5   

    B)        5.9   

    C) 163      

    D)        110.8

    Correct Answer: A

    Solution :

    [a] Horizontal range = \[\frac{{{\text{u}}^{2}}\sin 2\theta }{g}\text{ so g}\propto {{\text{u}}^{2}}\] \[\text{or   }\frac{{{\text{g}}_{\text{planet}}}}{{{\text{g}}_{\text{earth}}}}=\frac{{{\left( {{\text{u}}_{\text{planet}}} \right)}^{2}}}{{{\left( {{\text{u}}_{\text{earth}}} \right)}^{2}}}\] \[\text{Therefore }{{\text{g}}_{\text{planet}}}={{\left( \frac{3}{5} \right)}^{2}}\left( 9.8\text{ m/}{{\text{s}}^{2}} \right)\] \[=3.5\text{ m/}{{\text{s}}^{2}}\]       


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