A solid sphere of mass M and radius R is kept on a rough surface. The velocities of air (density ρ) around the sphere are as shown in figure. Assuming R to be small and M = , what is the minimum value of coefficient of friction so that the sphere starts pure rolling? (Assume force due to pressure difference is acting on centre of mass of the sphere)

Engineering

Physics

BernoulIis Equation and Equation of Continuity

Question

A solid sphere of mass M and radius R is kept on a rough surface. The velocities of air (density ρ) around the sphere are as shown in figure. Assuming R to be small and M = $\frac{4 {πρR}^{2}}{g} kg$ , what is the minimum value of coefficient of friction so that the sphere starts pure rolling? (Assume force due to pressure difference is acting on centre of mass of the sphere)

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Force due to pressure difference is F = $\frac{1}{2}$ ρπR² (v₂² – v₁²) = $\frac{7 {ρπR}^{2}}{2}$
Now, F – f = Ma
f_R = $\frac{2}{5}$ MR² × $\frac{a}{R}$
⟹ f = $\frac{2}{5}$ Ma ⟹ f = $\frac{2}{7}$ F = ρπR² ⟹ μMg = πρR²

⟹ μ = $\frac{{πρR}^{2}}{Mg} = \frac{1}{4} = 0 .25$