Question

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
(1) 80%
(2) 40%
(3) 96%
(4) 120%​

Answer 1

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 %