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Question

A mass M is suspended as shown in figure. If the system is in equilibrium and K is the spring constant, then the extension produced in the spring is given by (assume pulleys to be massless and strings inextensible.)


  1. 4MgK
  2. MgK
  3. 2MgK
  4. 3MgK


Solution

The correct option is A 4MgK

Let extension in spring be X,
From diagram, we get,
T1=Mg   .......(1) 
T2=T1+T1=2T1   ......(2)
KX=T2+T2=2T2   ......(3)
Therefore, from (2) and (3)
KX=4T1
Now, using (1), we get
KX=4Mg
X=4MgK
Hence option A is correct

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