MPSC CIVIL ENGINEERING 2020

Mechanics  

Q.59.  When a body is in equilibrium, then which statements are cirrect?

1. Summation of moment about any point is equal to zero (i.e ΣM = 0)
2. Summation of forces along any direction is equal to zero (i.e ΣF = 0)
3. Summation of moment is not equal to zero (i.e ΣM ≠ 0)
4. Summation of forces is not equal to zero (i.e ΣM ≠ 0)

Ans - 1 and 2

Solution -

The body is said to be in equilibrium if the resultant of all forces acting on it is zero. There are two major types of static equilibrium, namely, translational equilibrium and rotational equilibrium.

Formulas
Concurrent force system
ΣFx=0

ΣFy=0
 

Parallel Force System
ΣF=0

ΣMO=0
 

Non-Concurrent Non-Parallel Force System
ΣFx=0

ΣFy=0

ΣMO=0

Equilibrium of Concurrent Force System

In static, a body is said to be in equilibrium when the force system acting upon it has a zero resultant.

 (A) Conditions of Static Equilibrium of Concurrent Forces

The sum of all forces in the x-direction or horizontal is zero.  

$\mathrm{\Sigma }{F}_x=0$   or   ΣFH=0

The sum of all forces in the y-direction or vertical is zero.

F$\mathrm{\Sigma }{F}_y=0$   or    ΣFV=0

Important Points for Equilibrium Forces

• Two forces are in equilibrium if they are equal and oppositely directed.
• Three coplanar forces in equilibrium are concurrent.      

Equilibrium of Parallel Force System

   (B)  Conditions for Equilibrium of Parallel Forces

             The sum of all the forces is zero.

                                       ΣF=0 

          The sum of moment at any point O is zero.   

                              ΣMO
ΣMO=0