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  4. Two blocks of masses m and M are attached to the two ends of a light string passing over a fixed ideal pulley (M gg m). When the blocks are in motion, the tension in the string is approximately

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Q. Two blocks of masses $m$ and $M$ are attached to the two ends of a light string passing over a fixed ideal pulley $(M \gg m)$. When the blocks are in motion, the tension in the string is approximately

Laws of Motion

Solution:

Let $a$ be the common acceleration of the system and
$T$ be the tension in the string.
The equation of motion for the block $m$ is
$T-m g=m a \quad \ldots$ (i)
The equation of motion for the block $M$ is
$M g-T=M a \ldots$ (ii)
Adding $(i)$ and $(ii)$, we get
$M g-m g=m a+M a$
or $ a=\left(\frac{M-m}{m+M}\right) g$
image
Substituting this value in $(i)$, we get
$T=\frac{2 M m}{M+m} g $
$\because M \gg m, m$ can be neglected as it is very small when compare to $M$
$\therefore T \approx 2 m g$