Question

The system of the wedge and the block connected by a massless spring as show in the figure is released with the spring in its natural length. Friction is absent. Maximum elongation in the spring will be

• A. $\frac{3Mg}{5k}$
• B. $\frac{6Mg}{5k}$
• C. $\frac{4Mg}{5k}$
• D. $\frac{8Mg}{5k}$

Answer 1

The correct option is B $\frac{6Mg}{5k}$

The equilibrium position of the given system will be given by
$[m\times g\times sin(37)=k\times x]$

$\left[\right(m\times g\times sin37)/k=x]$

Now the block is at its extreme position in the beginning, hence maximum elongation will be given by,$\left[\right(2\times m\times g\times sin37)/k=x]$.

$x=\frac{6mg}{5k}$. Since $sin37=3/5$