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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 on :
Both $A$ and $R$ are true but $R$ is NOT the correct explanation of $A$
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
$A$ is false but $R$ is true
$A$ is true but $R$ is false
Solution
Terminal velocity of a spherical body in liquid
$\Rightarrow V _{ t } \propto r ^2$
$\Rightarrow \frac{\Delta V _{ t }}{ V _{ t }}=2 \cdot \frac{\Delta r }{ r }$
$\Rightarrow \frac{\Delta V _{ t }}{ V _{ t }} \times 100 \%=2 \frac{(0.1)}{5} \times 100=4\,\%$
Also $V_t \propto r^2$
Reason $R$ is false
