Question

The system is pushed by a force F as shown in figure. All surfaces are smooth except between B and C. Friction coefficient between B and C is $\mu$. Minimum value of F to prevent block B from downward slipping is

• A. $\left(\frac{3}{2\mu }\right)mg$
• B. $\left(\frac{5}{2\mu }\right)mg$
• C. $\left(\frac{5}{2}\right)\mu mg$
• D. $\left(\frac{3}{2}\right)\mu mg$

Answer 1

Answer: (B)

Horizontal acceleration of the system is
$a=\frac{F}{2m+m+2m}=\frac{F}{5m}...\left(i\right)$
Let N be the normal reaction between B and C.Free body diagram of C gives
$N=2ma=\frac{2}{5}F$ (Using (i))
Now B will not slide downward if
$\mu N\ge \mu Bg$
or $\mu \left(\frac{2}{5}F\right)\ge mg$ or $F\ge \frac{5}{2\mu }mg$
So $F_{min}=\frac{5}{2\mu }mg$