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=3N,Y=3N
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B
X=0,Y=6N
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C
X=6N,Y=3N
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D
X=6N,Y=6N
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Solution
The correct option is DX=6N,Y=6N
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+6−6−X=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=6N From Eq (i),X=Y ⇒Y=6N