In the following arrangement, the system initially held at rest by an external agent. At $t = 0$ , the 5kg block is released. If the acceleration of block C is $\frac{x}{10} m s^{- 2}$ , then find the value of $x$ . Assume that the pulleys and strings are massless and smooth $[g = 9.8 m s^{- 2}]$ .

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Detailed Solution

Block B will not move

$5 g - T = 5 a \dots (i)$

$2 T - 8 g = 8 \frac{a}{2} \dots (i i)$

$2 g = 14 a$

$a = \frac{g}{7}$

$∴ \frac{a}{2} = \frac{g}{14} = \frac{9.8}{14} = \frac{7}{10} m s^{- 2} = 0.7$

$∴ x = 7$

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