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​

Answer 1

Kinetic energy depends upon the square of Velocity.

Thus, Relative Error in kinetic energy = Relative Error in mass + 2 x Relative Error in velocity

It should be noted, that 2 is multiplied because the power of the velocity is 2 in the formula of kinetic energy.

Since, about mass, nothing is given.

Thus we will assume the error in mass to be zero.

∴ Relative error in Kinetic energy = 2 × Relative error in speed

∴ ΔK.E./K.E. = 2 × ΔV/V

∴ ΔK.E./K.E. = 2 × 40

∴ ΔK.E./K.E. = 80%

Hence, the Relative error in the measurement of Kinetic energy is 80%.

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