Question

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. 

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The Correct Option is C

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 $\boxed{(3)}$.