Two masses 8; kg and 12; kg are connected at | vedclass

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(D) Let the masses be $m_1 = 8\; kg$ and $m_2 = 12\; kg$. The system is connected by a light inextensible string over a frictionless pulley.Since $m_2

Vedclass · Accepted Answer

$2\; m/s^2$ and $96\; N$

Vedclass · Answer

(D) Let the masses be $m_1 = 8\; kg$ and $m_2 = 12\; kg$. The system is connected by a light inextensible string over a frictionless pulley.Since $m_2 > m_1$,the mass $m_2$ moves downward with acceleration $a$,and $m_1$ moves upward with the same acceleration $a$.Applying Newton's second law of motion:For mass $m_1$: $T - m_1 g = m_1 a$  --- $(i)$For mass $m_2$: $m_2 g - T = m_2 a$  --- $(ii)$Adding equations $(i)$ and $(ii)$:$(m_2 - m_1) g = (m_1 + m_2) a$$a = \left( \frac{m_2 - m_1}{m_1 + m_2} ight) g = \left( \frac{12 - 8}{12 + 8} ight) 	imes 10 = \frac{4}{20} 	imes 10 = 2\; m/s^2$Now,substitute $a$ into equation $(ii)$ to find tension $T$:$T = m_2(g - a) = 12(10 - 2) = 12 	imes 8 = 96\; N$Thus,the acceleration is $2\; m/s^2$ and the tension is $96\; N$.

Two masses $8\; kg$ and $12\; kg$ are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.

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