Question

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

• A. $\frac{mMg}{nm+M}$
• B. $\frac{mMg}{nmM}$
• C. $mg$
• D. $mng$

Answer 1

The correct option is A $\frac{mMg}{nm+M}$

Let the tension in the string connecting $n^{th}$ mass be $T_n$
The given system may be represented as combined mass of $nm$ having acceleration $a$ as indicated in the figure.

$Mg-T=Ma$ ............ (1)

From the FBD of combined system of $n$ blocks,
$T=nma$ ............ (2)
From Eqs. (1) and (2)
$a=\frac{Mg}{nm+M}$
FBD of $n^{th}$ block,

$T_n=ma=\frac{mMg}{nm+M}$