The system is released form rest with both the springs in unstretched position. Mass of each block is 1 kg and force constant of each spring is 10 N/m. Assume pulleys and strings are massless and all contacts are smooth.Then which of the following is incorrect. (g = 10 m/s²)

• A

  Extension of horizontal spring in equilibrium is 2/5 m
• B

  Extension of vertical spring in equilibrium is 1/5 m
• C

  Maximum speed of the block A is $\sqrt{\frac{8}{5}}m/s$
• Correct answer
  D

  Maximum speed of the block A is $\sqrt{14}m/s$

Solution

The system is released...


         
                  

 $\text{T}=2\text{kx}\Rightarrow 5\text{kx}=\text{mg}$

$\text{x}=\frac{\text{mg}}{5\text{k}}=\frac{1\times 10}{5\times 10}=\frac{1}{5}$

(ii) $\left(1\right)\left(\text{g}\right)\left(\text{x}\right)=\frac{1}{2}\left(1\right){\left(\text{v}\right)}^2+\frac{1}{2}\left(1\right){\left(2\text{v}\right)}^2\text{x}+\frac{1}{2}\left(10\right){\left(\text{0.2}\right)}^2+\frac{1}{2}\left(10\right){\left(\text{0.4}\right)}^2$

$2=\frac{{\text{V}}^2}{2}\left(1+4\right)+\frac{1}{2}\left(\text{0.4}+\text{1.6}\right)\Rightarrow \text{v}=\sqrt{\frac{2}{5}}$

${\text{v}}_{\text{A}}=2\text{v}=\sqrt[2]{\frac{2}{5}}=\sqrt{\frac{8}{5}}$

So only wrong option is (iv)

Hence, the correct answer is option: 'D'.