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NEET PHYSICSMechanical Properties of FluidEasy

Question

The velocity of a small ball of mass MM and density dd, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2d/2, then the viscous force acting on the ball will be:

A

3Mg/23Mg/2

B

2Mg2Mg

C

Mg/2Mg/2

D

MgMg

Step-by-Step Solution

When the ball's velocity becomes constant, it has reached its terminal velocity, a state where the net force acting on the object is zero , . In this equilibrium state, the downward force of gravity (weight, WW) is perfectly balanced by the sum of the upward forces: the buoyant force (BB) and the viscous force (FvF_v) .

  1. Weight (WW): Given as W=MgW = Mg.
  2. Buoyant Force (BB): This force is equal to the weight of the displaced fluid. Since the ball has mass MM and density dd, its volume is V=M/dV = M/d . The density of glycerine is given as d/2d/2. Therefore, B=V×(d/2)×g=(M/d)×(d/2)×g=Mg/2B = V \times (d/2) \times g = (M/d) \times (d/2) \times g = Mg/2 .
  3. Equilibrium Equation: At terminal velocity, Fv+B=WF_v + B = W. Substituting the values, we get Fv+Mg/2=MgF_v + Mg/2 = Mg.
  4. Result: Solving for the viscous force, Fv=MgMg/2=Mg/2F_v = Mg - Mg/2 = Mg/2.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Mechanical Properties of Fluid. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMechanical Properties of Fluidvelocitydensitydroppedcontainerfilled

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