Question

Two identical blocks A and B, each of mass $m=2kg$ are connected to the ends of an ideal spring having force constant $k=1000N{m}^{-1}$. System of these blocks and spring is placed on a rough floor. Coefficient of friction between blocks and floor is $\mu =0.5$. Block B is pressed towards left so that spring gets compressed.
Initial minimum compression $x_0$ of spring such that block A leaves contact with the wall when system is released is:

• A. $3cm$
• B. $4cm$
• C. $5cm$
• D. $6cm$

Answer 1

The correct option is A $3cm$

Block A will move when the extension on the spring $x_f=\mu mg/k$

Initial state: $x_i$ compression. Total displacement of block B : $x_i+x_f$

Initial Energy : $\frac{1}{2}k{x}_i^2$

Final Energy : $\frac{1}{2}k{x}_f^2$

Work Done : (By friction) : $\mu mg(x_i+x_f)$

Change in energy = Work done by external forces.

$\mu mg(x_i+x_f)=\frac{1}{2}k(x_i^2-x_f^2)$

$2\mu mg/k+x_f=x_i$

$x_i=3\mu mg/k=0.03m=3cm$