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JEE Main & Advanced Sample Paper JEE Main Sample Paper-22

  • question_answer
    Two metallic spheres \[{{S}_{1}}\] and \[{{S}_{2}}\] are made of same material and have got identical surface finish. The mass of \[{{S}_{1}}\] is thrice that of \[{{S}_{2}}\] Both of the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of initial rate of cooling of \[{{S}_{1}}\] to that of \[{{S}_{2}}\] is:

    A)  \[{{\left( \frac{1}{3} \right)}^{1/3}}\]               

    B)  \[{{\left( \frac{1}{3} \right)}^{1/2}}\]

    C)  \[\frac{1}{3}\]                         

    D)  \[\sqrt{3}\]

    Correct Answer: A

    Solution :

    \[\frac{\Delta Q}{\Delta T}=e\sigma A{{T}^{4}}\] \[\frac{\Delta Q}{\Delta T}=e\sigma A{{T}^{4}}=\frac{mc\Delta T}{\Delta t}\] \[A=\pi {{r}^{2}}\,=\pi {{\left( \frac{3m}{4\pi \rho } \right)}^{2/3}}\] from \[m=\frac{4}{3}\pi {{r}^{3}}\rho \] \[\left( \frac{\Delta T}{\Delta t} \right)\propto \,{{\left( \frac{1}{m} \right)}^{1/3}}\]            \[\frac{(\Delta T/\Delta t)}{{{(\Delta T/\Delta t)}_{2}}}={{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}^{1/3}}\,={{\left( \frac{1}{3} \right)}^{1/3}}\]


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