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The kinetic energy of a body is determined from measurements of its momentum p and its mass m.The percentage uncertainties in the measurements are:p± 3%m±4%What is the percentage uncertainty in the kinetic energy?A. 7%B. 10%C. 13%D. 14%

Question

The kinetic energy of a body is determined from measurements of its momentum p and its mass m.The percentage uncertainties in the measurements are:p± 3%m±4%What is the percentage uncertainty in the kinetic energy?A. 7%B. 10%C. 13%D. 14%

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Solution

The kinetic energy (K.E.) of a body is given by the equation K.E. = p^2 / 2m.

The percentage uncertainty in a quantity derived from other quantities is given by the sum of the percentage uncertainties in those quantities, each multiplied by the power to which it is raised in the formula.

In this case, the kinetic energy is proportional to the square of the momentum (p^2) and inversely proportional to the mass (1/m).

So, the percentage uncertainty in the kinetic energy is given by:

2 * (percentage uncertainty in p) + 1 * (percentage uncertainty in m)

= 2 * 3% + 1 * 4%

= 6% + 4%

= 10%

So, the percentage uncertainty in the kinetic energy is 10%. Therefore, the correct answer is B. 10%.

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