A spool of mass M = 3 kg and radius R = 20 cm has an axle of radius r = 10 cm around which a string is wrapped. The moment of inertia about an axis perpendicular to the plane of the spool and passing

Question

A spool of mass M = 3 kg and radius R = 20 cm has an axle of radius r = 10 cm around which a string is wrapped. The moment of inertia about an axis perpendicular to the plane of the spool and passing through the centre is M R 2 2 . If the coefficient of friction between the surface and the spool is 0 . 4 then the maximum tension which can be applied to the string for which the spool doesn't slip, is g = 10 m s - 2

TestHub · Accepted Answer

Writing the torque about the instantaneous axis of rotation we get,

$τ = T \times (R - r) = (\frac{M R^{2}}{2} + M R^{2}) α$

$\Rightarrow T = (\frac{3 M R^{2}}{2 (R - r)}) \frac{a}{R}$

Also,

$T - μ M g = M a$

Substituting the values and solving for $T$ we get,

$T = 18 N$

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion