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Q.

Two identical rollers each of weight W = 500 N are supported by an inclined plane and a vertical wall as shown in diagram. Assuming all surfaces are smooth , A,B,C and D are contact points
  
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a

Reaction induced at D,  250N

b

Reaction induced at A,  2503N

c

Reaction induced at C,  10003N

d

Reaction induced at B,  12503N

answer is A, B, C, D.

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Detailed Solution

 FA=2503N,FB=12503NandFC=10003N
 Question Image
Let FD  be the force of interaction (reaction) between the rollers. Consider the  equilibrium of upper roller: we have
  Fx=0. or FD500sin30=0
or  FD=500sin30=250 N
and   Fy=0. or FA500cos30=0
 Question Image
or    FA=500cos30=50032=2503 N
Now consider the equilibrium of lower roller ;
  Fx=0, or FCcos30FD500sin30=0
or   FC×32250500×12=0
or  FC=10003 N
and   Fy=0
or  FBFCsin30500cos30=0
or   FB10003×12500×32=0
or  FB=12502 N

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