Question

System shown in figure is released from rest. Pulley and spring is mass less and friction id absent everywhere. The speed of 5 kg block when 2 kg bock leaves the contact with ground is (Take force constant of spring k = 40 N/M and g = 10 ms^{-2})

• A. $\sqrt{2}{m}^{-1}$
• B. $2\sqrt{2}{m}^{-1}$
• C. $2m{s}^{=1}$
• D. $4\sqrt{2}{m}^{-1}$

Answer 1

The correct option is B $2\sqrt{2}{m}^{-1}$

$\begin{array}{c}\text{Correct option is}\left(B\right)\\ \text{When}2\text{kg block leaves the contact with}\\ \text{ground}N=0,T=mg\\ =20N\end{array}$

$\begin{array}{cc}\text{Extension}\Rightarrow \text{Fspring}& =T\\ kx& =20\\ x& =1/2m\end{array}$

$\begin{array}{cc}\text{Work}& =K_f-K_i\\ \text{Wravity}+{\omega }_{\text{spring}}& =k_f-0\\ Mgx-\frac{1}{2}K{x}^2& =\frac{1}{2}m{v}^2\\ 2\sqrt{2}& =V\end{array}$