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1st Equation of Motion

Two masses ...

Question

Two masses $m_{1}$ and $m_{2}$ are attached to string which pass over a frictionless fixed pulley. Given that $m_{1} = 10 k g$ and $m_{2} = 6 k g$ and $g = 10 {m s}^{- 2}$ . What is the acceleration of the masses?

2.5 {m s}^{- 2}

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5 {m s}^{- 2}

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20 {m s}^{- 2}

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40 {m s}^{- 2}

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Solution

The correct option is A $2.5 {m s}^{- 2}$
As the pulley is frictionless so the magnitude of the acceleration both masses are equal.

From FBD,

For $m_{1} : m_{1} a = m_{1} g - T . . . (1)$

For $m_{2} : m_{2} a = T - m_{2} g . . . (2)$

$(1) + (2)$

$a (m_{1} + m_{2}) = g (m_{1} - m_{2})$

or $a = \frac{m_{1} - m_{2}}{m_{1} + m_{2}} g = \frac{10 - 6}{10 + 6} 10 = 2.5 m / s^{2}$

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Two masses m1 and m2 are attached to string which pass over a frictionless fixed pulley. Given that m1=10kg and m2=6kg and g=10ms−2. What is the acceleration of the masses?

The correct option is A 2.5ms−2As the pulley is frictionless so the magnitude of the acceleration both masses are equal.From FBD, For m1:m1a=m1g−T...(1)For m2:m2a=T−m2g...(2)(1)+(2) a(m1+m2)=g(m1−m2)or a=m1−m2m1+m2g=10−610+610=2.5m/s2

Two masses $m_{1}$ and $m_{2}$ are attached to string which pass over a frictionless fixed pulley. Given that $m_{1} = 10 k g$ and $m_{2} = 6 k g$ and $g = 10 {m s}^{- 2}$ . What is the acceleration of the masses?