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BHU PMT BHU PMT Solved Paper-2001

  • question_answer
    A stationary object at \[4{}^\circ C\]and weighing 3.5 kg falls from a height of 2000 m on a snow mountain at\[0{}^\circ \,C\]. If the temperature of the object just before hitting the snow is \[0{}^\circ \,C\] and the object comes to rest immediately \[\left( g=10\,\,m/{{s}^{2}}\,\,and\,\,latent\,\,heat\,\,of\,\,ice=3.5\times {{10}^{5}}\,J/s \right),\] then the object will melt:

    A)  \[2\,\,kg\,\,of\,ice\]                     

    B)  \[200\,\,g\,\,of\,ice\]

    C)  \[20\,\,g\,\,\,ice\]                         

    D)  \[2\,\,g\,\,\,ice\]

    Correct Answer: B

    Solution :

    Key Idea: Law of conservation of energy is valid. Potential energy is the energy possessed by a body due to its height. It is given by \[PE=mgh\] Where \[m\] is mass, \[g\] is acceleration due to Gravity and \[h\] is height. This potential energy is utilized in giving latent heat \[\left( m'\,L \right)\] to ice.                 \[\therefore \]                                  \[m'L=mgh\] Given, \[m=3.5\text{ }kg,\] \[g=10\text{ }m\text{/}{{s}^{2}},\] \[h=2000\text{ }m,\] \[L=3.5\times {{10}^{5}}J\text{/}s.\] \[\therefore \]                  \[m'=\frac{mgh}{L}\] \[\Rightarrow \]                               \[m'=\frac{3.5\times 10\times 2000}{3.5\times {{10}^{5}}}\] \[\Rightarrow \]                               \[m'=0.2\,kg\,\]of ice Also, \[1\text{ }kg={{10}^{3}}g\] \[\therefore \]\[m'=200\,g\] of ice.


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