Question

A sphere of weight 50 N is resting in a V - shaped groove as shown in figure and is subjected to a spring force. The spring is compressed to a length of 120 mm from the free length of 160 mm. If the stiffness of spring is 2 N/mm the diffrence (magnitude, correct two decimal place) of the support reactions is ____.

• A. 47

Answer 1

The correct option is A 47
Spring force $=k\times \Delta x$
$=2(160-120)=80N$
Free body diagram of sphere:

From Lami's theorem
$\frac{R_A}{\sin {120}^{\circ }}=\frac{R_B}{\sin {150}^{\circ }}=\frac{130}{\sin {90}^{\circ }}$
$R_A=130\sin {120}^{\circ }=112.58N$
$R_B=130\sin {150}^{\circ }=65N$
$R_A-R_B=112.58-65=47.58N$