question_answer

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 \[\mu \]so that the sphere starts pure rolling. (\[Take\,g=10m/{{s}^{2}}\])  

A) \[\sqrt{3}\times 0.16\]

B) \[\sqrt{3}\times 0.08\]

C) \[\sqrt{3}\times 0.1\]

D) Data insufficient

Correct Answer: B

Solution :

[b] \[10\cos {{30}^{o}}-f=2a\] ?(i) \[\tau =I\alpha \] \[\Rightarrow \,\,\,{{f}_{r}}=\frac{2}{3}\times 2\times {{r}^{2}}\times \alpha \]   ? (ii) (where r is radius of sphere)           From (i) and (ii), we get \[f=2\sqrt{3}\] newton, \[N=20+10\sin \,\,{{30}^{o}}=25\] \[f=\mu N\Rightarrow \mu =\frac{f}{N}=\frac{2\sqrt{3}}{25}=0.08\times \sqrt{3}\]