Question

A block of mass $5kg$ is released from rest when compression in spring is $2m$. Block is not attached with the spring and natural length of the spring is $4m$. Maximum height of block from ground is $(g=10m/s^2)$

• A. $5.5m$
• B. $4.5m$
• C. $6m$
• D. $7.5m$

Answer 1

The correct option is A $5.5m$

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By energy conservation, initially total mechnical energy of system is,
$P{E}_{spring}+P{E}_{mass}=\frac{1}{2}k{x}^2=mgh=\frac{1}{2}\times 300\times 2^2+5\times 10\times 1=650J$

At the final condition, when block reaches its final position, let velocity = $v$ and height = $h$.
Height of floor = $6\times sin\left({30}^o\right)$= $3m$
Due to no further displacement $P{E}_{spring}=0$
Hence energy at final position, $P{E}_{mass}+KE=5\times 10\times 3+\frac{1}{2}\times 5\times v^2=650J\therefore v=10\sqrt{2}m/s$
By using the projectile motion equation height that will be attended by the block,
$H=\frac{v^{2}si{n}^2{30}^o}{2g}=2.5m$
So, total height from ground= $3+2.5$= $5.5m$