A) 6, 12
B) 11, 7
C) 5, 13
D) 14, 4
E) 10, 8
Correct Answer: C
Solution :
Let smaller force be\[{{F}_{1}}\]. Resultant R of the forces is at\[90{}^\circ \]to AB, \[\therefore \,\,{{R}^{2}}\,+F_{1}^{2}\,=F_{2}^{2}\] in \[\Delta \,ABC\] or \[{{(12)}^{2}}=F_{2}^{2}-F_{1}^{2}\] ...(i) or \[144=({{F}_{2}}-{{F}_{1}})({{F}_{2}}-{{F}_{1}})\] but \[{{F}_{1}}+{{F}_{2}}=18\,N\] (given)... (ii) \[\therefore \] \[{{F}_{2}}-{{F}_{1}}=\frac{144}{18}=8\] ??(iii) From Eqs. (ii) and (iii), \[{{F}_{1}}=5,\text{ }{{F}_{2}}=13\] Hence, forces are 5 N and 13 N.You need to login to perform this action.
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