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Two block ( 1 and 2 ) of equal mass \( m \) are connected by an ideal string (see figure below) over a frictionless pulley. The blocks are attached to the ground by springs having spring constants \( k_{1} \) and \( k_{2} \) such that \( k_{1}k_{2} \) :
Initially, both springs are unstretched. The block 1 is slowly pulled down a distance \( x \) and released. Just after the release the possible value of the magnitudes of the acceleration of the blocks \( a_{1} \) and \( a_{2} \) can be [KVPY 2012]
(a) Either \( \left(a_{1}=a_{2}=\frac{\left(k_{1}+k_{2}\right)}{2 m}\right) \) or \( \left(a_{1}=\frac{k_{1} x}{m}-g\right) \) and
\[
\left(a_{2}=\frac{k_{2} x}{m}+g\right)
\]
(b) \( \left(a_{1}=a_{2}=\frac{\left(k_{1}+k_{2}\right) x}{2 m}\right) \) only
(c) \( \left(a_{1}=a_{2}=\frac{\left(k_{1}-k_{2}\right) x}{2 m}\right) \) only
(d) Either \( \left(a_{1}=a_{2}=\frac{\left(k_{1}-k_{2}\right)}{2 m}\right) \) or
\[
\left(a_{1}=a_{2}=\frac{\left(k_{1} k_{2}\right)}{\left(k_{1}+k_{2}\right) m}-g\right)
\]
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