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A mass $m_{1}$ lies on fixed, smooth cylinder. An ideal cord attached to $m_{1}$ passes over the cylinder and is connected to mass $m_{2}$ as shown in the figure. Given $m_{1} = 5 k g, m_{2} = 4 k g .$ The system is released from rest when $θ = 30^{0}$ . Find the magnitude of acceleration in $m / s^{2}$ of mass $m_{1}$ just after the system is released. $(T a k e g = 10 m / s^{2})$

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Detailed Solution

Let the tangential acceleration of $m_{1}$ be $a .$
$∴ m_{2} g - m_{1} g \sin θ = (m_{1} + m_{2}) a$
$a = \frac{40 - 25}{9} = \frac{15}{9} m / s^{2}$
the normal acceleration of $m_{1}$ is zero.
speed of m₁ is zero.
The magnitude of acceleration of $m_{1} = \frac{15}{9} m / s^{2} .$

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A mass m1 lies on fixed, smooth cylinder. An ideal cord attached to m1 passes over the cylinder and is connected to mass m2 as shown in the figure. Given m1=5kg,m2=4kg. The system is released from rest when θ=300. Find the magnitude of acceleration in m/s2of mass m1 just after the system is released. (Take g=10m/s2)