Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : A spherical body of radius (5 ± 0.1) mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4%. Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.
Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A
A is true but R is false
A is false but R is true
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The Correct Option isC
Solution and Explanation
The terminal velocity (\( V_t \)) of a spherical body falling through a liquid is directly proportional to the square of its radius (\( r^2 \)):
\[
V_t \propto r^2.
\]
The percentage error in terminal velocity can be calculated using the formula:
\[
\frac{\Delta V_t}{V_t} = 2 \cdot \frac{\Delta r}{r}.
\]
Given:
\[
r = 5 \, \text{mm}, \quad \Delta r = 0.1 \, \text{mm}.
\]
Substitute the values:
\[
\frac{\Delta V_t}{V_t} \times 100 = 2 \cdot \frac{\Delta r}{r} \times 100 = 2 \cdot \frac{0.1}{5} \cdot 100 = 4\%.
\]
Hence, Assertion A is true.
However, the Reason R states that the terminal velocity is inversely proportional to the radius, which is incorrect because \( V_t \propto r^2 \). Therefore, Reason R is false.
Thus, the correct answer is \( \boxed{(3)} \).