NEET Physics Question - Unit And Dimensions

Assertion (A): The error in measurement of radius of the sphere is 0.3%. The permissible error in its surface area is 1.2%.

Reason (R): Area of sphere, \(A = 4\pi r^2 \Rightarrow \frac{\Delta A}{A} = 4\frac{\Delta r}{r}\).

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

The surface area of a sphere is \(A = 4\pi r^2\), which gives the fractional error relation as \(\frac{\Delta A}{A} = 2\frac{\Delta r}{r}\). Thus, the error in area is \(2 \times 0.3% = 0.6%\), making both statements false.

Rankers Physics

Permissible error in sphere surface area

Solution:

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