Question

A cylinder of radius $r=1m$ and mass $m=5\times {10}^{3}kg$ is at rest on the edges of a structure as shown. Distance $a=0.5m$ and $b=\frac{\sqrt{3}}{2}m$. Reaction force on edges $A$ and $B$ are:

• A. $24.6kN,24.6kN$
• B. $42.6kN,42.6kN$
• C. $42.6kN,24.6kN$
• D. $52.6kN,5.6kN$

Answer 1

Answer: (C)

$42.6kN,24.6kN$

Here, $\sin \theta =\frac{a}{r}=\frac{0.5}{1}=\frac{1}{2}\Rightarrow \theta ={30}^o$
and $\sin \theta {}^{\prime }=\frac{b}{r}=\frac{\sqrt{3}}{2}=\Rightarrow \theta {}^{\prime }={60}^o$
Reaction force on edge A is $F=mg\cos \theta =5\times {10}^3\times 9.8\times cos30=42.6kN$
Reaction force on edge B is $F^{\prime }=mg\cos \theta {}^{\prime }=5\times {10}^3\times 9.8\times cos60=24.6kN$