Question

Each of the two blocks shown in the figure has a mass \(m\). The coefficient of friction for all surfaces in contact is \(\mu\). A horizontal force \(P\) is applied to move the bottom block. The value of \(P\), for which acceleration of block \(A\) is same in both cases is

• A. $2\mu mg$
• B. $\mu mg$
• C. $3\mu mg$
• D. $\frac{2}{3}\mu mg$

Answer 1

The correct option is A $2\mu mg$


$a_1=\frac{P(\mu mg+2\mu mg)}{m}$
$=\left(\frac{P3\mu mg}{m}\right)$
$T-f_1=m{a}_2$
$P-T-f_2-f_1=m{a}_2$
$P-f_2-2f_1=2m{a}_2$
$a_2=\left(\frac{P4\mu mg}{2m}\right)$
For $2P-6\mu mg=P-4\mu mg$
$P=2\mu mg$