Question

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 $\sqrt{\frac{8}{5}}m/s$
• D. Maximum speed of the block A is $\sqrt{14}m/s$

Answer 1

Answer: (D)

The system is released...



$T=2kx\Rightarrow 5kx=mg$
$x=\frac{mg}{5k}=\frac{1\times 10}{5\times 10}=\frac{1}{5}$ ...(ii)
$(1)(g)(x)=\frac{1}{2}(1)(v{)}^2+\frac{1}{2}(1)(2v{)}^{2}x+\frac{1}{2}(10)(0.2{)}^2$
$+\frac{1}{2}(10)(0.4{)}^2$
$2=\frac{(V{)}^2}{2}(1+4)+\frac{1}{2}(0.4+1.6)$
$\Rightarrow v=\sqrt{\frac{2}{5}}$
$v_A=2v=\sqrt[2]{\frac{2}{5}}=\sqrt{\frac{8}{5}}$
So only wrong option is (iv)