Two blocks A & B connected by an ideal spring of constant 100 N/m and moving on a smooth horizon- tal surface under influence of a force of 36 N. What is extension in spring when acceleration of 2kg block is twice that of 5kg block?

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Spring force is internal; the 2 kg block has $a_{2} = 2 a$ and the 5 kg block $a_{5} = a$ (given). Spring force on the 2 kg block: $F_{s p} = 2 \times 2 a = 4 a$ .

For the 5 kg block: $36 - F_{s p} = 5 a \Rightarrow 36 - 4 a = 5 a \Rightarrow a = 4 m/ s^{2}$ , $F_{s p} = 16 N$ .

Extension $= \frac{16}{100} m = 16 cm$ .

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