Question 262: Laws of Motion

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

Accepted Answer

Horizontal acceleration of the system
$$a=\frac{F}{2 m+m+2 m}=\frac{F}{5 m}$$
Let $$N$$ be the normal reaction between $$B$$ and $$C$$. Free body diagram of $$C$$ gives,
$$N=2 m a=\frac{2}{5} F$$
Now, $$B$$ will not slide downward
If $$\mu N \geq m_B g$$
or $$\quad \mu\left(\frac{2}{5} Fight) \geq m g$$ or $$F \geq \frac{5}{2 \mu} m g$$
or $$F_{	ext {min }}=\frac{5}{2 \mu} mg$$

Answer

$$\left(\frac{3}{2 \mu}\right) m g$$

Answer

$$\left(\frac{5}{2 \mu}\right) m g$$

Answer

$$\left(\frac{5}{2}\right) \mu m g$$

Answer

$$\left(\frac{3}{2}\right) \mu m g$$

Laws of Motion

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

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