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  4. In the following arrangement, the system is initially held at rest by an external agent. At t=0 , the 5kg block is released. If the acceleration of block C is (x/10)ms- 2 , then find the value of x . Assume that the pulleys and strings are massless and smooth. [ g=9.8 ms- 2 ] <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-l3xeintebubi.png />

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

Question

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

Block B will not move
$5g-T=5a$ ...(i)
$2T-8g=8\frac{a}{2} \, $ ...(ii)
Solution
$2g=14a$
$a=\frac{g}{7}$
$\therefore \frac{a}{2}=\frac{g}{14}=\frac{9.8}{14}=\frac{7}{10}ms^{- 2}=0.7$
$\therefore x=7$