Kinetic energy of a particle depends on the squareof speed of the part

1.	Kinetic energy of a particle depends on the squareof speed of the particle. If error in measurement ofspeed is 40% then error in the measurement ofkinetic energy will be(1) 80%(2) 40%(3) 96%(4) 120%
Answer» Answer: 96% kinetic energy of a particle depends on square of speed of a particle. e.g., K =1/2 mv² .(1)LET initial velocity of a particle is v and initial kinetic energy is K. if ERROR of speed is 40% then new speed of particle ,v' = v + 40% of v = y + 40v/100 = 1.4v then kinetic energy will be K' = 1/2 mv'2 = 1/2 m(1.4v)2 = 1/2 m(1.96v) = (1.96) 1/2mv? = (1.96) K [ FORM equation (1), ] now, % error in Kinetic energy = final kinetic energy- initial kinetic energy/initial kinetic energy x 100 = (K' K)/K x 100 = = = (1.96K - K)/K 100 = 0.96K/K x 100 = 96% *hence, maximum error in kinetic energy about be 96 %*

Kinetic energy of a particle depends on the squareof speed of the particle. If error in measurement ofspeed is 40% then error in the measurement ofkinetic energy will be(1) 80%(2) 40%(3) 96%(4) 120%

Answer»

Answer: 96%

kinetic energy of a particle depends on square of speed of a particle.

e.g., K =1/2 mv²

.(1)LET initial velocity of a particle is v and initial kinetic energy is K.

if ERROR of speed is 40%

then new speed of particle ,v' = v + 40% of v

= y + 40v/100 = 1.4v

then kinetic energy will be K' = 1/2 mv'2

= 1/2 m(1.4v)2

= 1/2 m(1.96v)

= (1.96) 1/2mv?

= (1.96) K [ FORM equation (1), ]

now, % error in Kinetic energy = final kinetic energy- initial kinetic energy/initial kinetic energy x 100

= (K' K)/K x 100 =

= = (1.96K - K)/K 100

= 0.96K/K x 100

= 96%

hence, maximum error in kinetic energy about be 96 %

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