Question

50 Blocks with each having mass = 2 kg one connected by light strings as shown. If topmost block is pulled with a force F = 2000 N, then tension in the rope connecting 48th and 49th block. [Assume all block to be in air]

Answer 1

Let $\sf{m_i=2\ kg}$ be the mass of $\sf{i^{th}}$ block.

Total mass of the system would be,

$\sf{\longrightarrow M=50\times2\ kg}$

$\sf{\longrightarrow M=100\ kg}$

The applied force is given by,

$\sf{\longrightarrow F=M(a+g)}$

$\sf{\longrightarrow 2000=100(a+10)}$

$\sf{\longrightarrow a=10\ m\,s^{-2}}$

This is the net acceleration of the system.

The tension in the rope connecting $\sf{48^{th}}$ and $\sf{49^{th}}$ blocks is given by,

$\sf{\longrightarrow T=F-(m_1+m_2+\,\dots\,+m_{48})(a+g)}$

$\sf{\longrightarrow T=2000-48\times2\,(10+10)}$

$\sf{\longrightarrow \underline{\underline{T=80\ N}}}$

Hence 80 N is the answer.