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Question

A mass of 6 kg is suspended by a rope of length 2m from ceiling. A force of 60 N is applied in the horizontal direction at the mid-point of the rope. The angle made by the rope, with the vertical, in equilibrium position will be :

(Take g=10ms2, neglect the mass of the rope)

A
53
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B
60
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C
30
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D
45
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Solution

The correct option is D 45
Given,

Mass =6kg

Force =60N

Length of the rope =2m

Equilibrium of the given weight with gravitational force acting on it gives,

T2=6×10=60N

There are three forces acting on the mass tension 1 (T1) and tension 2 (T2) and the force acting horizontally, that is, 60N

The resultant force will be vertical and horizontal components acting separately vanish to become one force

Hence,

T1cosθ=T2=60N

and

T1sinθ=60N

60sinθ=60cosθ

tanθ=1

θ=tan11=450

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