Figure shows N identical blocks connected with identical strings on a smooth horizontal surface. A constant force is pulling the blocks horizontally. If tension in string connecting 4th and 5th block is two times that between 8th and 9th block what is total number of blocks.

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TestHub · Accepted Answer

Each block has mass m (identical) and the surface is smooth, so the whole train moves with a = F/(Nm). The string between the k-th and (k+1)-th block pulls the last (N - k) blocks:

$T_{k} = (N - k) m \times \frac{F}{Nm} = \frac{( N - k ) F}{N}$

Given T_4 = 2 T_8:

$N - 4 = 2 (N - 8) \Rightarrow N - 4 = 2 N - 16 \Rightarrow N = 12$

Correct option: (D).

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