First slide

Friction on horizontal surface

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 $μ$ . Minimum value of F to prevent block B from downward slipping is:

Moderate

A

$(\frac{3}{2 μ}) mg$
B

$(\frac{5}{2 μ}) mg$
C

$(\frac{5}{2}) μmg$
D

$(\frac{3}{2}) μmg$

Solution

Horizontal acceleration of the system is
$a = \frac{F}{2 m + m + 2 m} = \frac{F}{5 m}$
Let N be the normal reaction between B and C. Free body diagram of C gives
$N = 2 ma = \frac{2}{5} F$
Now, B will not slide downward if 1 $μ$ N $\geq m_{B} g$
or $μ (\frac{2}{5} F) \geq mg or F \geq \frac{5}{2 μ} mg$
or $F_{\min} = \frac{5}{2 μ} mg$

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