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Standard XII

Physics

Simple Harmonic Oscillation

A block of ma...

Question

A block of mass $m_{1}$ is connected with another block of mass $m_{2}$ by a light spring. $m_{2}$ is connected with a hanging mass $m_{3}$ by an inextensible light string. At the time of release of block $m_{3}$ :

tension in the string is

(\frac{m_{2} m_{3}}{m_{2} + m_{3}}) g

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acceleration of

m_{1}

0

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acceleration of

m_{3}

(\frac{m_{3}}{m_{1} + m_{2} + m_{3}}) g

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acceleration of

m_{3}

(\frac{m_{3} - m_{2}}{m_{1} + m_{2}})

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Solution

The correct option is C acceleration of $m_{3}$ is $(\frac{m_{3}}{m_{1} + m_{2} + m_{3}}) g$
We have taken ( $m_{1} + s p r i n g + m_{2}$ ) as a combined system. By doing so we need not bother to take spring effect as the spring forces now become internal forces which will cancel each other.
For block 3; $m_{3} a = m_{3} g - T$ .............(1)
For combined system; $(m_{1} + m_{2}) a = T$ .............(2)
$m_{3} a = m_{3} g - (m_{1} + m_{2}) a ⟹ a = (\frac{m_{3}}{m_{1} + m_{2} + m_{3}}) g$
Also, from (2), $T = \frac{(m_{1} + m_{2}) (m_{3} g)}{(m_{1} + m_{2} + m_{3})}$

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A block of mass m1 is connected with another block of mass m2 by a light spring. m2 is connected with a hanging mass m3 by an inextensible light string. At the time of release of block m3:

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