Question

The coefficient of static friction between the two blocks is $0.363$, what is the minimum acceleration of block $1$ so that block $2$ does not fall ?


[Take $g=9.8{\text{m/s}}^2$]

• A. $6{\text{m/s}}^2$
• B. $12{\text{m/s}}^2$
• C. $18{\text{m/s}}^2$
• D. $27{\text{m/s}}^2$

Answer 1

The correct option is D $27{\text{m/s}}^2$

For no slipping, limiting friction should be more than the weight of block 2.

FBD of block $2:$


From FBD, we get
At limiting condition,
$f=mg$ and $N=ma$

$\therefore \mu N=mg$

$\Rightarrow \mu ma=mg$

$\Rightarrow a_{\text{min}}=\frac{g}{\mu }=\frac{9.8}{0.363}=27{\text{m/s}}^2$

Hence, option $\left(d\right)$ is correct.