A hollow sphere of mass 2 kg is kept on a rough horizontal surface. A force of 10 N is applied at the centre…
A hollow sphere of mass 2 kg is kept on a rough horizontal surface. A force of 10 N is applied at the centre of the sphere as shown in the figure. Find the minimum value of \(\mu\) so that the sphere starts pure rolling. (take \(g=10 \mathrm{~ms}^{-2}\))
$\sqrt{3} \times 0.16$
$\sqrt{3} \times 0.08$
$\sqrt{3} \times 0.1$
Data insufficient
Solution
$10 \cos 30^{\circ}-f=2 a$... (i)
$\tau=I \alpha$
$\Rightarrow f r=\frac{2}{3} \times 2 \times r^{2} \times \alpha \ldots$ (ii)
(where $r$ is radius of sphere) From (i) and (ii), we get $f=2 \sqrt{3}$ newton,
$N=20+10 \sin 30^{\circ}=25$
$f=\mu \mathrm{N} \Rightarrow \mu=\frac{f}{N}=\frac{2 \sqrt{3}}{25}=0.08 \times \sqrt{3}$
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