Rotational Motion Question 200
Question: 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 . Find the minimum value $\mu $ so that the sphere starts pure rolling. ($Takeg=10m/s^{2}$ )
Options:
A) $\sqrt{3}\times 0.16$
B) $\sqrt{3}\times 0.08$
C) $\sqrt{3}\times 0.1$
D) Data insufficient
Show Answer
Answer:
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,
$N=20+10\sin 30^{o}=25$
$f=\mu N\Rightarrow \mu =\frac{f}{N}=\frac{2\sqrt{3}}{25}=0.08\times \sqrt{3}$
