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 $\frac{M R^{2}}{2}$ . 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 $\left[g = 10 \, m \, s^{- 2}\right]$

• A. $24N$
• B. $18N$
• C. $9N$
• D. $36N$

Answer 1

Answer: (B)

Writing the torque about the instantaneous axis of rotation we get,
$\tau=T\times \left(R - r\right)=\left(\frac{M R^{2}}{2} + M R^{2}\right)\alpha $
$\Rightarrow T=\left(\frac{3 M R^{2}}{2 \left(R - r\right)}\right)\frac{a}{R}$
Also,
$T-\mu Mg=Ma$
Substituting the values and solving for $T$ we get,
$T=18N$