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 : option (3) 96

explanation : 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

= v + 40v/100 = 1.4v

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

= 1/2 m(1.4v)²

= 1/2 m(1.96v²)

= (1.96) 1/2mv²

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

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%

hence, maximum error in kinetic energy should be 96%