Question

System shown in figure is released from rest pulley and spring is massless and friction is absent everywhere. The speed of 5kg block when 2 kg block leaves the contact with ground is given by $n\sqrt{2}$ m/sec then find the value of n, (K=40N/m & g=10$m/s^2$)

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

$\begin{array}{c}\text{Correct option is}\left(B\right)\\ \text{When}2kg\text{leaves ground}\\ \begin{array}{cc}T& =mg\\ T& =2g\\ & =20N\\ \text{so;}T=& F_{\text{Spring}}\\ 20& =Kx\\ 1/2& =x\end{array}\end{array}$

$\begin{array}{c}\text{Work}=k_f-k_i\left(\text{for}5kg\right)\\ {\omega }_g+{\omega }_s=k_f\\ mgx-\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2\end{array}$

$\begin{array}{cc}50-10& =5v^2\\ 2\sqrt{2}m/s& =v\\ 2\sqrt{2}& =n\sqrt{2}\\ 2& =n\end{array}$