Assertion A: A spherical body of radius 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%. [2023]

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Solution

Q.
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 $(5 \pm 0.1)$ 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.

In the light of the above statements, choose the correct answer from the options given below [2023]

1 Both A and R are true but R is NOT the correct explanation of A

2 Both A and R are true and R is the correct explanation of A

3 A is false but R is true

4 A is true but R is false

Ans.
(4)

$Terminal velocity of a spherical body in liquid$

$\Rightarrow V_{t} \propto r^{2} \Rightarrow \frac{Δ V_{t}}{V_{t}} = 2 \cdot \frac{Δ r}{r}$

$\Rightarrow \frac{Δ V_{t}}{V_{t}} \times 100 % = 2 \frac{0.1}{5} \times 100 = 4 %$

$Also V_{t} \propto r^{2}$

$Reason R is false$

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