JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer A body is thrown vertically upwards from the surface of earth in such a way that it reaches upto a height equal to \[10{{R}_{e}}\]. The velocity imparted to the body will be

    A)  \[10.6\,km/s\]               

    B)  \[0.106\,km/s\]

    C)  \[1.06\,km/s\]               

    D)  zero

    Correct Answer: A

    Solution :

     Work done in going from a distance \[{{r}_{1}}\] to a distance \[{{r}_{2}}\]away from centre of the earth, by a body of mass m, is, \[W=GMm(1/{{r}_{1}}-1/{{r}_{2}}),\] For our case we should have \[1/2m{{v}^{2}}=GMn[(1/{{R}_{e}})-(1/10{{R}_{e}})]\] \[=(GMm/{{R}_{e}})\times (9/10)\] \[v=\sqrt{{}}[(2GM/{{R}_{e}})\times (9/10)]=\sqrt{{}}(9/10)\times \]escape velocity \[\sqrt{{}}(9/10)\times 11.1km/s=10.6km/s\]

adversite


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