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Applied Mechanics - Engineering

Q1:

A weight W is suspended at the free end of a light member hinged to a vertical wall. If the angle of inclination of the member with the upper wall is θ°, the force introduced in the member, is

A W sec θ

B W cos θ

C W sin θ

D W cosec θ

E W tan θ.

ANS:A - W sec θ

When a weight W is suspended at the free end of a light member hinged to a vertical wall and the member makes an angle θ with the upper wall, the force introduced in the member can be analyzed using trigonometric relationships and principles of equilibrium. Let's denote the force introduced in the member as T. This force T has two components:

  1. Vertical Component: T cos θ
  2. Horizontal Component: T sin θ
The vertical component T cosθ balances the weight W acting downwards. Therefore, we have: T cos θ = W From this, we can solve for T: T=W / cosθ Therefore, the force introduced in the member is W / cosθ, which corresponds to option W sec θ. So, the correct answer is: W secθ.