A block of mass 10kg is moving in x-direction with a constant speed of 10 m/s . It is subjected to a retarding force F=-0.1 x joule / meter during its travel from x=20 meter to x=30 meter. Its final kinetic energy will be.
 

  • Option 1)

    475 J 

  • Option 2)

    450 J 

  • Option 3)

    275 J

  • Option 4)

    250 J

 

Answers (1)
P Plabita

As we discussed in Concept

Net work done by all the forces give the change in kinetic energy -

W=\frac{1}{2}mv^{2}-\frac{1}{2}mv{_{0}}^{2}

W= k_{f}-k_{i}

- wherein

m=mass \: of\: the\: body

v_{0}= initial\: velocity

v= final\: velocity

 

 

 W=k_{f}-k_{i}

=> k_{f}=W+k_{i}

k_{f}=\int_{x_{1}}^{x_{2}}fxdx+\frac{1}{2}mv^{2}

=>\int_{30}^{20}-0.1\times dx+\frac{1}{2} 10\times 10^{2}

=-0.1\left [ \frac{x^{2}}{2} \right ]^{30}_{20}+500

=-0.50\left [ 30^{2}-20^{2} \right ]+500

=-0.05\left [ 900-400 \right ]+500

k_{f}=-25+500=475J

 


Option 1)

475 J 

Option is correct

Option 2)

450 J 

Option is incorrect

Option 3)

275 J

Option is incorrect

Option 4)

250 J

Option is incorrect

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