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  4. In the given arrangement, n number of equal masses are connected by strings of negligible masses. The tension in the string connected to n th mass is

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Q. In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to $n$ th mass is

Laws of Motion

Solution:

The system may be represented as follow
image
From the force diagram,
$M g-T=M a\,\,\,...(i)$
and$T=n m a\,\,\,...(ii)$
From Eqs. (i) and (ii), we get
$a=\frac{M g}{n m+M}$
The force diagram of $n$ th block is shown in figure.
image
From the figure,
$T_{n}=m a =\frac{m M g}{n m+M}$