NEET Physics MCQs

The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv + kr^2v^2$. The dimensions of $k$ are:

The dimensions of coefficient of viscosity are:

The viscous force $F$ acting on a sphere moving through a liquid depends on the radius $r$ of the sphere, the velocity $v$ of the sphere, and the coefficient of viscosity $η$ of the liquid. If $F = kη^arv^b$, where $k$ is a dimensionless constant, using dimensional analysis, find the values of $a$, $b$.

The viscous force $F$ acting on a sphere of radius $r$ moving with velocity $v$ through a fluid of viscosity $\eta$ is given by $F = 6\pi \eta rv$. If a new physical quantity $Q$ is defined as $Q = \frac{Fv^2}{\eta^2 r^3}$, the dimensions of $Q$ are:

Which limitation of dimensional analysis prevents it from deriving the complete formula for the viscous force on a sphere moving through a fluid, given that the force (F) depends on the radius (r) of the sphere, its velocity (v), and the fluid's viscosity ($\eta$)?

Which of the following factors does not directly affect the viscous force acting on a spherical object moving through a viscous fluid according to Stokes' Law?

A small solid sphere of radius 'r' and density 'ρ' falls under gravity in a viscous fluid of density 'σ' and coefficient of viscosity 'η'. If $\rho > \sigma$, and the sphere has attained terminal velocity, which of the following changes would result in a decrease in the terminal velocity, assuming all other factors remain constant?

Two identical spheres, A and B, are released simultaneously from the same height in two different viscous liquids. Sphere A reaches terminal velocity faster than sphere B. Which of the following conclusions can be drawn about the liquids?

Two spherical balls of radii $r_1$ and $r_2$ ($r_1 < r_2$) are falling through a viscous fluid with terminal velocities $v_1$ and $v_2$ respectively. If the densities of the balls are the same and Stokes' Law applies, which of the following relationships is correct?

A small metal sphere of radius 'r' and density 'ρ' falls from rest in a viscous liquid of density 'σ' and coefficient of viscosity 'η'. Which expression represents the time 't' it takes for the sphere to attain one-half of its terminal velocity (neglecting buoyancy)?