Question

A mass 35 kg is suspended from a weightless bar AB which is supported by a cable CB and a pin at A as shown in figure. The pin reactions at A on the bar AB are

• A. $R_x=343.4N,R_y=755.4N$
• B. $R_x=343.4N,R_y=0$
• C. $R_x=755.4N,R_y=343.4N$
• D. $R_x=755.4N,R_y=0$

Answer 1

The correct option is D $R_x=755.4N,R_y=0$

Since point A is hinge support, so there will be horizontal and vertical reactions at point A.

For block $T_2=mg=343.35N...\left(i\right)$

$\tan \theta =\frac{125}{275}=0.4545$

$\theta ={\tan }^{-1}\left(0.4545\right)={24.44}^{\circ }$

For bar $\Sigma M_A=0$

$T_1\sin \theta \times l=T_2\times l$

$\Rightarrow T_1=\frac{T_2}{\sin \theta }=\frac{343.35}{\sin {24.44}^{\circ }}$

$=829.74N$

$\Sigma F_y=0$

$+R_y-T_2+T_1\sin \theta =0$

$\Sigma F_x=0$

$R_x-T_1\cos \theta =0$

$R_x=755.39N$