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Question

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


A

450J

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B

475J

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C

250J

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D

275J

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Solution

The correct option is B

475J


Step1: Kinetic energy

  1. Kinetic energy is the energy created by an object as a result of its motion.
  2. When an object is set to accelerate, it is imperative that specific forces be applied.
  3. Work is required to apply force, and once the work is completed, the energy is transmitted to the object, causing it to move at a constant velocity.

Step2: Given data

Block of mass, m=10kg

Regarding force, F=0.1xJ/m and it is acted on the block from x=20cmtox=30cm

Step3: Formula used

K.E=12mv2[whereK.E=kineticenergy,m=mass,v=velocity]

Since the force F is a variable force, The work small amount of work done in moving the block to a small distance (dx) is given by,

dW=Fdx

Step4: Calculating kinetic energy

K.E.=12mv2K.E.=12×10×(10)2K.E.=500J

Step5: Calculating work done

Further, it is given to us that the block is subjected to a retarding force. Since the force F is a variable force, The work small amount of work done in moving the block to a small distance (dx) is given by,

dW=FdxdW=20300.1xdxW=0.12030xdxW=0.1x222030W=0.05[302-202]W=0.05[900-400]W=25J

Step6: Calculating final kinetic energy

K.E(Final)=K.E-WK.E(Final)=500-25K.E(Final)=475J

Hence, option B is the correct answer.


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