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Question

Two blocks $$1$$ and $$2$$ of masses $$2m$$ and $$m$$ are suspended by means of a massless spring and a massless inextensible string as shown in the figure. The acceleration of blocks $$1$$ and $$2$$ immediately after the string is cut are respectively.
828516_3c0c9622a02c40b0a605ae15764956c0.png


A
g,g
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B
g,g2
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C
g2,2g
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D
g,g
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Solution

The correct option is B $$g\uparrow, \dfrac {g}{2}\downarrow$$
Just before the string in cut, force on the spring pulling $$up=kx=3mg$$
Therefore after string is cut, free body diagram of block $$A$$
$$\begin{array}{l} \therefore 2m{ a_{ A } }=3mg-2mg \\ or\, \, { a_{ A } }=\dfrac { { mg } }{ { 2m } } =\dfrac { g }{ 2 }  \\ Free\, \, body\, \, diagram\, of\, \, block\, B \\ \therefore m{ a_{ B } }=mg \\ or\, \, { a_{ B } }=g \end{array}$$

Physics

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