Assertion (A): In streamline flow streamlines never intersect each other.
Reason (R): If streamline intersect then their must two velocities of fluid particle at the point of intersection, which is impossible.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is true by definition of streamline flow.
Reason (R) is true because intersection would imply multiple velocity vectors at a single point, which is physically impossible.
(R) correctly explains (A).
Assertion (A): The stream of water emerging from a water tap “necks down” as it falls.
Reason (R): The volume flow rate at different levels is same.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Concept: Continuity equation for fluid flow. For an incompressible fluid in steady flow, the volume flow rate \(AV\) (Area × Velocity) must remain constant. As water falls, its velocity \(V\) increases due to gravity, therefore, its cross-sectional area \(A\) must decrease, causing it to 'neck down'. Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
The viscous drag acting on a metal sphere of diameter \(1 \text{mm}\), falling through a fluid of viscosity \(0.8 \text{Pa} \text{s}\) with a velocity of \(2 \text{m} \text{s}^{-1}\) is equal to
1. \(1.5 \times 10^{-3} \text{N}\)
2. \(20 \times 10^{-3} \text{N}\)
3. \(15 \times 10^{-3} \text{N}\)
4. \(30 \times 10^{-3} \text{N}\)
View Answer
Using Stokes' Law: \(F = 6\pi\eta r v\). Here, \(r = 0.5 \times 10^{-3} \text{m}\), \(\eta = 0.8 \text{Pa} \text{s}\), and \(v = 2 \text{m/s}\). \(F = 6 \times \pi \times 0.8 \times 0.5 \times 10^{-3} \times 2 \approx 15 \times 10^{-3} \text{N}\).