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. 

Updated On: Mar 20, 2025
  • 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 is C

Solution and Explanation

The terminal velocity (Vt V_t ) of a spherical body falling through a liquid is directly proportional to the square of its radius (r2 r^2 ): Vtr2. V_t \propto r^2. The percentage error in terminal velocity can be calculated using the formula: ΔVtVt=2Δrr. \frac{\Delta V_t}{V_t} = 2 \cdot \frac{\Delta r}{r}. Given: r=5mm,Δr=0.1mm. r = 5 \, \text{mm}, \quad \Delta r = 0.1 \, \text{mm}. Substitute the values: ΔVtVt×100=2Δrr×100=20.15100=4%. \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 Vtr2 V_t \propto r^2 . Therefore, Reason R is false. Thus, the correct answer is (3) \boxed{(3)} .
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