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 $\sqrt{1 4} m/s$

Answer 1

Answer: (D)

The system is released...



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