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Question

A long uniform beam is acted upon by several forces as shown in figure, and it is in complete equilibrium. What will be the value of forces X & Y? Neglect the mass of the beam.


A
X=3 N,Y=3 N
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B
X=0,Y=6 N
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C
X=6 N,Y=3 N
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D
X=6 N,Y=6 N
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Solution

The correct option is D X=6 N,Y=6 N

For the complete equilibrium of the body, net external force as well as net external torque should be zero.

For translational equilibrium of body,
Fnet=0
Considering upwards direction as +ve
F=0
Y+66X=0
Y=X ...(i)
For rotational equilibrium, the net torque be zero about point B:
τnet=0 ...(ii)
τ=F×r
Force Y passes through reference point B, hence torque τY=0 about point B.
Taking anticlockwise sense of rotation for torque as +ve and substituting the torque with proper sign in Eq (ii),
τ=0
+X(30)+0+6(10)6(40)=0
X=18030=6 N
From Eq (i),X=Y
Y=6 N

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