Two uniform spheres of same radius have point charges 2µC embedded at their centres. Appreciable friction exists between spheres and plank so that they can roll purely but ground is smooth. Find the acceleration (in m/s2) of plank just after the system is released.

Engineering

Physics

Static and Kinetic Friction

Rolling

Charge and Coulombs Law

Question

Two uniform spheres of same radius have point charges 2µC embedded at their centres. Appreciable friction exists between spheres and plank so that they can roll purely but ground is smooth. Find the acceleration (in m/s²) of plank just after the system is released.

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F – f = ma
f.R = I $\frac{a}{R}$
F – f = m $(\frac{f R^{2}}{I})$

$f [1 + \frac{{mR}^{2}}{I}] = F$

$f = \frac{F}{(1 + \frac{{mR}^{2}}{I})}$