Question

Block A of mass m and block B of mass M are cooected by a massless spring over a puuey on a rough plane with coefficient of friction as $\mu$. A force F is applied on block A to the left. Find the minimum value of M to move the block A towards right.

• A. $\frac{F}{2g}+\frac{\mu m}{2}$
• B. $\frac{F}{g}+\mu m$
• C. $\frac{F}{2g}+\mu m$
• D. $\frac{F}{3g}+\mu m$

Answer 1

The correct option is B $\frac{F}{g}+\mu m$

Let $x$ is expansion on the string it occurs a force $Kx$

$F+u m g=k x \rightarrow i$

$kx=Mg\to ii$

from (i) and (ii)

$Mg=F+\mu mg$

$M=\frac{F}{g}+\frac{\mu mg}{g}$

$M=\frac{F}{g}+\mu m$

$\text{(B)}\frac{F}{g}+\mu m$