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CMC Medical CMC-Medical VELLORE Solved Paper-2009

  • question_answer
    A stone is thrown vertically upwards. When stone is at a height half of its maximum height, its speed is 10 \[m{{s}^{-1}},\] then the maximum height attained by the stone is (g = 10 \[m{{s}^{-2}}\])

    A)  5 m                                       

    B)  150 m

    C)  20 m                                    

    D)  10 m

    Correct Answer: D

    Solution :

                     Let u be the initial velocity and h be the maximum height attained by the stone. \[v_{1}^{2}={{u}^{2}}-2g{{h}_{1}}\] \[\therefore {{(10)}^{2}}={{u}^{2}}-2\times 10\frac{h}{2}\,\left( \because {{h}_{1}}=\frac{h}{2},\,{{v}_{1}}=10\,m{{s}^{-1}} \right)\] or \[100={{u}^{2}}-10\,h\]                            ?(i) Again at height h, \[v_{2}^{2}={{u}^{2}}-2gh\] \[0={{u}^{2}}-2\times 10\times h\]          \[(\because {{v}_{2}}=0)\] \[0={{u}^{2}}-20h\]                         ?(ii) Subtracting Eq. (ii) from Eq. (i), we get \[100=10\,h\] or            \[h=\frac{100}{10}=10\,m\]


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