MHT CET · Physics · Mechanical Properties of Fluids
A small ball of mass \(M\), radius \(R\) and density \(\rho\) moves with terminal velocity through a container filled with glycerine of density \(\sigma\). The viscous force acting on the ball is ( \(g=\) gravitational acceleration)
- A Мgрб
- B \(M g(\rho-\sigma)\)
- C \(M g\left[1-\frac{\sigma}{\rho}\right]\)
- D \(\frac{M g \rho}{\sigma}\)
Answer & Solution
Correct Answer
(C) \(M g\left[1-\frac{\sigma}{\rho}\right]\)
Step-by-step Solution
Detailed explanation
Considering force balance on the ball falling with terminal velocity:
\(F_v+\sigma V g=\rho V g\)
where \(F_v\) is the viscous force, \(V\) is the volume of the ball.
Taking the ratio of equation (1) and (2):
\(F_v=M g\left(1-\frac{\sigma}{\rho}\right)\)
\(F_v+\sigma V g=\rho V g\)
where \(F_v\) is the viscous force, \(V\) is the volume of the ball.
Taking the ratio of equation (1) and (2):
\(F_v=M g\left(1-\frac{\sigma}{\rho}\right)\)
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