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  4. Two blocks of masses 8 kg and 12 kg are connected at the two ends of a light inextensible string. The string passes over a frictionless pulley. The acceleration of the system is

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Q. Two blocks of masses $8 \,kg$ and $12\, kg$ are connected at the two ends of a light inextensible string. The string passes over a frictionless pulley. The acceleration of the system is

KEAMKEAM 2011Laws of Motion

Solution:

Let $a$ be the common acceleration of the system and $T$ be tension of the string. The equations of motion of two blocks are
$T-8g=8a$ $\quad\ldots\left(i\right)$
and $12g-T=12a$ $\quad\ldots\left(ii\right)$image
Adding (i) and (ii), we get
$4g=20a$ $\quad$ or $ a=\frac{g}{5}$