NEETPhysicsMechanical Properties of Fluids
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
Options
- ABoth A and R are true and R is the correct explanation of A
- BBoth A and R are true but R is NOT the correct explanation of A
- CA is true but R is false
- DA is false but R is true
Correct answer
C. A is true but R is false
Step-by-step solution
The terminal velocity is V T = 2 9 r 2 g ρ - ρ ' η ⇒ V T ∝ r 2 Differentiating and dividing by V T , ⇒ d V T V T = 2 d r r = 2 × 0 . 1 5 So, the percentage error is d V T V T × 100 = 0 . 2 5 × 100 = 4 % As can be seen the terminal velocity is directly proportional to the square of the radius. Hence A is true but R is false.