If the coefficient of friction between all surfaces is 0.4 then find the minimum force F applied to have system in equilibrium.
A
62.5N
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B
72.5N
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C
82.5N
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D
92.5N
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Solution
The correct option is A62.5N 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 15kg 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 25kg 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=125N
Putting this in (2), we get, F=62.5N