If the percentage errors in the measurements of mass, length and time are 1%, 2% and 3% respectively, then the maximum permissible error in the measurement of the acceleration of a particle is
- 8%
- 9%
- 6%
- 10%
- 2%
The Correct Option is A
Solution and Explanation
The formula for acceleration \( a \) is:
\[ a = \frac{v}{t} \]
Where: - \( v \) is the velocity, - \( t \) is the time. If the acceleration \( a \) is given by: \[ a = \frac{F}{m} \] where \( F \) is force and \( m \) is the mass. The percentage error in a product or quotient is the sum of the percentage errors in the individual quantities. Therefore, the percentage error in the acceleration is the sum of the percentage errors in mass, length, and time.
Given: - The percentage error in mass = 1%, - The percentage error in length = 2%, - The percentage error in time = 3%. The maximum permissible error in acceleration is: \[ \text{Percentage error in acceleration} = \text{Percentage error in mass} + \text{Percentage error in length} + \text{Percentage error in time} \] Substituting the given values: \[ 1\% + 2\% + 3\% = 8\% \]
Correct Answer:
Correct Answer: (A) 8%
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