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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Critical Thinking

  • question_answer
    A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is                                           [AMU 1995]

    A)             \[R/\left( \frac{gR}{2{{V}^{2}}}-1 \right)\]

    B)                      \[R\,\left( \frac{gR}{2{{V}^{2}}}-1 \right)\]

    C)             \[R/\left( \frac{2gR}{{{V}^{2}}}-1 \right)\]

    D)             \[R\left( \frac{2gR}{{{V}^{2}}}-1 \right)\]

    Correct Answer: C

    Solution :

                                \[\Delta K.E.=\Delta U\]             \[\Rightarrow \,\,\frac{1}{2}M{{V}^{2}}=G{{M}_{e}}M\,\left( \frac{1}{R}-\frac{1}{R+h} \right)\]            ?(i) Also \[g=\frac{G{{M}_{e}}}{{{R}^{2}}}\]                                  ?(ii) On solving (i) and (ii) \[h=\frac{R}{\left( \frac{2gR}{{{V}^{2}}}-1 \right)}\]


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