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Two blocks ( 1 and 2) of equal mass $m$ are connected by an ideal string (see figure shown) over a frictionless pulley. The blocks are attached to the ground by springs having spring constants $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$ such that $\mathrm{k}_{1}>\mathrm{k}_{2}$
Initially, both springs are unstretched. The block 1 is slowly pulled down a distance $\mathrm{x}$ and released. Just after the release the possible values of the magnitude of the acceleration of the blocks $a_{1}$ and $a_{2}$ can be-
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Initially, both springs are unstretched. The block 1 is slowly pulled down a distance $\mathrm{x}$ and released. Just after the release the possible values of the magnitude of the acceleration of the blocks $a_{1}$ and $a_{2}$ can be-
Solution:
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Verified Answer
The correct answer is:
$\left(a_{1}=a_{2} \frac{\left(k_{1}+k_{2}\right) x}{2 m}\right)$ only
$\begin{array}{l}
\mathrm{T}+\mathrm{k}_{1} \mathrm{x}-\mathrm{mg}=\mathrm{ma}_{1} \\
\mathrm{k}_{2} \mathrm{x}+\mathrm{mg}-\mathrm{T}=\mathrm{ma}_{2}
\end{array}$
By constraint relation $\mathrm{a}_{1}=\mathrm{a}_{2}$
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