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Question

If the coefficient of friction between all surfaces is 0.4 then find the minimum force F applied to have system in equilibrium.


A
62.5 N
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B
72.5 N
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C
82.5 N
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D
92.5 N
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Solution

The correct option is A 62.5 N
Force has been applied along the horizontal direction, hence the minimum value of F will lead to the minimum value of normal reaction between all surfaces.
FBD of 15 kg block:


The block will tend to slip downward, therefore friction will act upwards.
Applying equilibrium condition along horizontal,
N=F ...........(1)
and along vertical,
T+f=150
T+μN=150
T+0.4N=150
T+0.4F=150 .........(2) [from (1)]
FBD of 25 kg block-


Applying equilibrium condition along horizontal,
N=N=F ...........(3)
and along vertical,
2T+f=250+f
2T+μN=250+μN
2T+μN=250+μN [from (3)]
T=125 N
Putting this in (2), we get,
F=62.5 N

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