A $12 kg$ monkey climbs a light rope as shown in fig. The rope passes over a pulley and is attached to a $16 kg$ bunch of bananas. Mass and friction in the pulley are negligible so that the effect of pulley is only to reverse the direction of force of the rope. What maximum acceleration can the monkey have without lifting the bananas? (Take $g = 10 m / s^{2}$ )

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$4 m / s^{2}$

$3.33 m / s^{2}$

$3 m / s^{2}$

$5.3 m / s^{2}$

answer is B.

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Detailed Solution

For Monkey,

$T - 120 = 12 \times a$ ... (i)
For Bananas
$160 - T = N$
Condition for just loosing the contact is $N = 0$
$160 - T = 0 \Rightarrow T = 160$ ...(ii)
From equation (i) & (ii)
$160 - 120 = 12 \times a \Rightarrow a = 3.33 m / s^{2}$

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