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RAJASTHAN PMT Rajasthan - PMT Solved Paper-2010

  • question_answer
    Two balls of masses \[{{m}_{1}}\] and\[{{m}_{2}}\] are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly the powder charge explodes and masses are pushed apart. The mass\[{{m}_{1}}\]travels a distance \[{{S}_{1}}\] and stops. If the coefficients of friction between the balls and ground are same, the mass \[{{m}_{2}}\]stops after travelling the distance

    A)  \[{{s}_{2}}=\frac{{{m}_{1}}}{{{m}_{2}}}{{s}_{1}}\]                            

    B)  \[{{s}_{2}}=\frac{{{m}_{2}}}{{{m}_{1}}}{{s}_{1}}\]

    C)  \[{{s}_{2}}=\frac{{{m}_{1}}}{m_{2}^{2}}{{s}_{1}}\]          

    D)         \[{{s}_{2}}=\frac{m_{2}^{1}}{m_{1}^{2}}{{s}_{1}}\]

    Correct Answer: C

    Solution :

    According to the question                 \[s\propto \frac{1}{{{m}^{2}}}\]                \[\therefore \]  \[\frac{{{s}_{2}}}{{{s}_{1}}}={{\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)}^{2}}\] or            \[{{s}_{2}}={{\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)}^{2}}\times {{s}_{1}}\]


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