Kinetic energy of a particle depends on the square of speed of the particle. If error in measurement of speed is 40% then error in the measurement of kinetic energy will be
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Solution
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Hint :
Error in kinetic energy is KΔK.
Step1:Initial Kinetic Energy
Kinetic energy of a particle depends on square of speed of a particle.
K=1/2mv2….(1)
Let initial velocity of a particle is v and initial kinetic energy is K
Step2:Final Speed of particle
If error in speed is40%
then new speed of particle v′=v+40% of v
=v+40v/100
=1.4v
Step3:Final Kinetic Energy
Final kinetic energy will be K′=1/2mv′2
=1/2m(1.4v)2
=1/2m(1.96v2)
=(1.96)1/2mv2
= (1.96) K [ form equation (1), ]
Step4:Error in Kinetic Energy
Now, % error in Kinetic energy = final kinetic energy− initial kinetic energy/initial kinetic energy×100
=(K′−K)/K×100
=(1.96K−K)/K×100
=0.96K/K×100
=96%
Therefore maximum error in kinetic energy should be 96%.