Two masses of $40 k g$ and $30 k g$ are connected by a weightless string passing over a friction less pulley as shown in the figure. The acceleration of the system would be:

0.6 m s^{- 2}

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0.8 m s^{- 2}

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0.7 m s^{- 2}

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0.5 m s^{- 2}

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Solution

The correct option is C $0.7 m s^{- 2}$
Gravitation force on A, $F_{A} = m g sin 30 = 40 \times 10 \times 0.5 = 200 N$

Gravitation force on B, $F_{B} = M g sin 30 = 30 \times 10 \times 0.5 = 150 N$

$F_{n e t} = F_{A} - F_{B}$

$\Rightarrow (M + m) a = F_{A} - F_{B}$

$\Rightarrow a = \frac{F_{A} - F_{B}}{M + m} = \frac{200 - 150}{40 + 30} = 0.71 m s^{- 2}$

Hence, acceleration of the system is $0.71 m {s^{-}}^{2}$

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