Question

Two blocks A of mass $10\text{kg}$ and block B are connected to each other as shown in the figure. The pulley is frictionless. The coefficient of friction between the surfaces is $0.3$. If the spring is stretched by $1\text{cm}$ and friction is maximum, Calculate the spring constant $\left(k\right)$ of the spring shown in the figure.

• A. $2000\text{N/m}$
• B. $3000\text{N/m}$
  
• C. $2500\text{N/m}$
• D. $3500\text{N/m}$

Answer 1

The correct option is B $3000\text{N/m}$



As block B is at rest.
$\therefore m_{B}g=kx=T..\left(i\right)$


Block A is also at rest.Therefore balancing forces along $y$ axis.
$N=m_{A}g$
We know maximum value of static friction is;$f_s=\mu N=\mu m_{A}g$
Balancing forces along $x$ axis gives.
$T=kx=\mu m_{A}g$
$\therefore k=\frac{\mu m_{A}g}{x}=\frac{0.3\times 10\times 10}{0.01}\text{N/m}=3000\text{N/m}$