Error Analysis

The formula for resistivity is given by:

The relative error in resistivity is given by:

Substituting the given values:

Calculating each term:

To find the percentage error in the physical quantity given by the relation , we use the formula for percentage error in a derived quantity:

• The percentage error in a physical quantity is obtained by summing the relative percentage errors of each variable multiplied by their respective powers.

Let's analyze each of the terms individually:

1. The power of in the expression is . Since the percentage error in is , the contribution of to the percentage error in will be .
2. The power of is . Thus, the contribution of to the percentage error in will be .
3. The power of is (because it is in the denominator, we take it as a negative value). Therefore, the contribution of to the percentage error in will be .

Therefore, the total percentage error in is:

Hence, the percentage error in is

Therefore, the correct answer is 34%.

To determine the percentage error in Young's modulus , we need to calculate the fractional errors in the mass and the extension and then combine them to find the error in .

The formula for Young's modulus is given by:

Let's assume that the errors in and are and respectively. The given smallest scale divisions are for and for . Thus, we have:

The values of and are given as and respectively.

The percentage error in any product or quotient is the sum of the percentage errors in each of the factors. Therefore, the percentage error in is given by:

Substituting the values, we get:

Therefore, the total percentage error in is:

Thus, the percentage error of is 2%.

Lens Formula and Derivative for Error Analysis:
The lens formula is given by:

Taking the derivative of both sides with respect to and , we get:

Rearranging for :

Error in Measurement of Focal Length:
Since and represent the measurement errors in and ,

respectively, we can substitute and :

Conclusion:
The error in the measurement of the focal length is:

The formula for the density of the wire is: where is the radius and is the length of the wire. The maximum percentage error in the density is given by: where and are the absolute errors in mass, radius, and length respectively.

Step 1: Calculate the percentage errors. - Percentage error in mass: , - Percentage error in radius: , - Percentage error in length: .

Step 2: Add the errors. The total percentage error in density:

Thus, the maximum percentage error in the measurement of the density is .

To find the percentage error in the measurement of C, we first need to understand how errors propagate through the given formula. The expression for C is:

C =

The percentage error formula for a product or quotient involving powers, given a function like , is:

Applying this to our expression:

• m = 1 for p
• n = 2 for q
• p = 3 for r
• q = 0.5 for √s (since )

The percentage error in C is:

Calculating this gives:

• 1% for p
• 4% for q
• 9% for r
• 1% for s (0.5 × 2%)

Add these errors together:

1% + 4% + 9% + 1% = 15%

Thus, the percentage error in the measurement of C is 15%, which is within the expected range of 15,15.