Question

A system is shown in figure. Blocks $2$ & $3kg$ are at rest, then coefficient of friction between $2kg$ and incline is:

• A. $2/\sqrt{3}$
• B. $1/2$
• C. $1/3$
• D. $Datainsufficient$

Answer 1

The correct option is A $2/\sqrt{3}$

$3g=T-FBDofblockofmass3kg$.

$T=2g\sin \theta +f$

$\Rightarrow f=3g-2g\sin \theta$

${\mu }^{2}g\cos \theta =3g-2g\sin \theta$

$\Rightarrow 2\mu \cdot \frac{\sqrt{3}}{2}=3-2\times \frac{1}{2}=2$.

$\Rightarrow \mu =\frac{2}{\sqrt{3}}$.

Now, this may not be maximum frictional force (Since, static friction is adjustable).

$\Rightarrow \mu \ge \frac{2}{\sqrt{3}}$.