The ends of spring are attached to blocks of mass 3 kg and 2 kg. The 3 kg block rests on a horizontal surface and the 2 kg block which is vertically above it is in equlibirium producing a compression of 1 cm Of the spring . The 2 kg mass must be compressed further by at least______, So that when it is released, the 3kg block may be lifted off the ground.

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Solution

Let the masses be $m_{1} = 2 k g$ and $m_{2} = 3 k g$
assume, spring constant $= k$
Given : Compression $x = 1 c m$
Force on spring $=$ weight of $m_{1}$
$\Rightarrow k x = m_{1} g \Rightarrow k = \frac{2 \times 10}{10^{- 2}} = 2000 N / m$
Let compression after exerting force be $y$
when force is removed the spring goes up, lifting $m_{2}$ upwards
Mean spring force $=$ sum of weights of $m_{1}$ and $m_{2}$
$\Rightarrow k g = 2 g + 3 g \Rightarrow 2000 y = 5 \times 10 g = 10 m / s \Rightarrow y = \frac{50}{2000} = 2.5 c m o r 0.025 m$

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