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Acceleration

Two masses ...

Question

Two masses $M_{1}$ and $M_{2}$ are attached to a string, which passes over a friction-less fixed pulley as shown in the fig. Given that $M_{1} = 10 k g, M_{2} = 6 k g a n d g = 10 m s^{- 2}$ . What is the acceleration of the masses?

40 m s^{- 2}

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20 m s^{- 2}

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5 m s^{- 2}

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2.5 m s^{- 2}

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Solution

The correct option is D $2.5 m s^{- 2}$
Let acceleration of system of mass is a
let $m_{1}$ is greater than $m_{2}$ then, acceleration of mass $m_{1}$
in downward and acceleration of mass $m_{2}$ in upward.
for mass $m_{1}$
$m_{1} g - T = m_{1} a$ ...................(1)
for mass $m_{2}$
$m_{2} g - T = m_{2} a$ ...................(2)
here, T is tension in string.
solve equation $(1)$ and $(2)$
$m_{1} g - m_{2} g = m_{1} a + m_{2} a$
$a = \frac{(m_{1} - m_{2}) g}{(m_{1} + m_{2})}$
now put value of $m_{1}$ , $m_{2}$
so, $\begin{matrix} a = \frac{(10 - 6) 10}{(10 + 6)} a = 2.5 m / s^{2} \end{matrix}$
Hence,
option $D$ is correct answer.

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Two masses M1 and M2 are attached to a string, which passes over a friction-less fixed pulley as shown in the fig. Given that M1=10kg,M2=6kg and g=10ms−2. What is the acceleration of the masses?

Two masses $M_{1}$ and $M_{2}$ are attached to a string, which passes over a friction-less fixed pulley as shown in the fig. Given that $M_{1} = 10 k g, M_{2} = 6 k g a n d g = 10 m s^{- 2}$ . What is the acceleration of the masses?