NEET Sample Paper NEET Sample Test Paper-21

  • question_answer A body of mass 2 kg has an initial speed of 5 m/s. A force acts on it for some time in the direction of motion. The force-time graph is shown in figure. The final speed of body is

    A) 9.25 m/s.                     

    B) 5 m/s.  

    C)   14.31 m/s.       

    D)                4.25 m/s.

    Correct Answer: C

    Solution :

    \[F=\frac{dP}{dt}\Rightarrow dP=Fdt\] \[\therefore \]\[\int_{{}}^{{}}{dP=\int_{{}}^{{}}{F\,dt}\Rightarrow \Delta \Pi }=\int_{{}}^{{}}{F\,dt}\] So the change in moment\[\Delta P\]is equal to the area under the curve \[\therefore \]\[\Delta P=\frac{1}{2}\times 2\times 4+4\times 2+\frac{1}{2}(4+2.5)\]\[\times \,0.5+2.5\times 2\] \[=4+8+\frac{6.5}{4}+5=18.625\] \[\Rightarrow \]\[{{P}_{2}}-{{P}_{1}}=18.625\,\Rightarrow \,{{P}_{2}}={{P}_{1}}+18.625\] \[\therefore \]\[m{{v}_{2}}=m{{v}_{1}}+18.625\] \[\Rightarrow \]\[{{v}_{2}}={{v}_{1}}+\frac{18.625}{2}=5+\frac{18.625}{2}\] \[=14.3125\,m/s.\] Hence, the correction option is (c).


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