Question 3.26: Two rollers of mass 20 kg and 10 kg rest on a horizontal bea...
Two rollers of mass 20 kg and 10 kg rest on a horizontal beam as shown in the Fig. 3.37 with a massless wire fixing the two centers. Determine the distance x of the load 20 kg from the support A, if the reaction at A is twice of that at B. The length of the beam is 2 m and the length of the connecting wire is 0.5 m. Neglect weight of beam. Assume the rollers to be point masses neglecting its dimensions.
(UPTU-2008)
Considering FBD of beam AB as shown in Fig. 3.37 (a)
\sum Y=0, \qquad R_{A}+R_{B}=20 \times g+10 \times g= 30 \times g
R_{A}+R_{B}=30 \times 9.81
Given that R_{A}= 2 R_{B}
\therefore \quad 2 R_{B}+R_{B}=30 \times 9.81
R_{B}=98.1 N \text { and } R_{A}=196.2 N
\sum M_{A}=0R_{B} \times 2=20 \times g \times x+10 \times g(x+0.5)
98.1 \times 2=20 \times g \times x+10 g \times x+10 g \times 0.5
20 = 20x + 10x +5
15 = 30x
x = 0.5 m
