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Two smooth blocks of same mass, connected by an inextensible and massless string which is passing over a smooth pulley, are kept in a lift as shown in figure. The lift is going down with an acceleration ‘a’ while block A moves horizontally with respect to the lift. What should be the value of a (in $m / s^{2}$ ) so that acceleration of block A with respect to ground will have minimum value?
(g = 10 $m / s^{2}$ )

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answer is 2.

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Detailed Solution

$a_{n e t} = \sqrt{{(\frac{g - a}{2})}^{2} + a^{2}}$
$\frac{\sqrt{g^{2} + 5 a^{2} - 2 a g}}{2}$
for $a_{n e t}$ to be min $a = \frac{g}{5}$

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