Correct Answer - Option 3 : 3
The correct answer is option 3) i.e. 3
CONCEPT:
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Combination of errors: When physical quantities involving a mathematical operation have errors associated with them, there will be an error in the result arising from its combination.
- This is identified based on the following rules:
- The error of a sum or a difference: If two physical quantities A and B have measured values A ± ΔA, B ± ΔB respectively where ΔA and ΔB are their absolute errors, the possible error ΔZ in the operation Z = A ± B is given by:
± ΔZ = ± ΔA ± ΔB
- The error of a product or a quotient: If two physical quantities A and B have measured values A ± ΔA, B ± ΔB respectively where ΔA and ΔB are their absolute errors, the possible error ΔZ in the operation Z = AB or Z = A ÷ B is given by:
\( \frac{\Delta Z}{ Z} = \frac{∆A}{A} + \frac{∆B}{B}\)
- The error in case of a measured quantity raised to a power:
If Z = Ax then
\(\frac{\Delta Z}{Z} = x\frac{\Delta A}{A}\)
CALCULATION:
We know that kinetic energy, \(KE = \frac{1}{2}mv^2\)
Given that: \(\frac{\Delta m}{m } = 2\% \), \(\frac{\Delta v}{v } = x\% \) and \(\frac{\Delta KE}{KE } = 8\% \)
So, using the rule for error of a product, \( \frac{\Delta KE}{ KE} = \frac{∆m}{m} +2 \frac{∆v}{v}\)
⇒ 8% = 2% + 2x%
⇒ 2x% = 8 - 2 = 6%
⇒ x% = 3%
Therefore, x = 3
