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JCECE Engineering JCECE Engineering Solved Paper-2005

  • question_answer
    A body is projected vertically upwards from the surface of a planet of radius r with a velocity equal to l/3rd the escape velocity for the planet. The maximum height attained by the body is:

    A)  \[R/2\]                                

    B)  \[R/3\]

    C)  \[R/5\]                                

    D)  \[R/9\]

    Correct Answer: D

    Solution :

    Key Idea: Escape velocity\[{{v}_{e}}=\sqrt{2gR}\] Let \[h\] be the maximum height attained, then from equation of motion                 \[{{v}^{2}}={{u}^{2}}+2gh\] When,  \[u=0,\,\,v=\sqrt{2gh}\] Given,   \[v=\frac{{{v}_{e}}}{3}\] where, \[{{v}_{e}}=\sqrt{2gR}\] \[\therefore \]    \[\sqrt{2gh}=\frac{1}{3}\sqrt{2gR}\] Squaring both sides of equation, we get                   \[h=\frac{R}{9}\]


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