Question

On a table, three blocks (including the first block) are placed as shown in figure. Mass of each block is $m$ and coefficient of friction for each block is $\mu$. The pulleys are smooth and massless. The strings are massless and inextensible. A force $F$ is applied on the leftmost block so as to move the system. The minimum value of $F$ should be

• A. $8\mu mg$
• B. $9\mu mg$
• C. $7\mu mg$
• D. $5\mu mg$

Answer 1

The correct option is C $7\mu mg$

For body to move (Right most)

$T_1=f_{max}{T}_1=\mu mg$

For middle body

$T_2=2T_1+f_{max}\Rightarrow T_2=2\mu mg+\mu mg\Rightarrow T_2=3\mu mg$

For leftmost block

$F=2T_2+f_{max}F=6\mu mg+\mu mgF=7\mu mg$