Question-55245

Question Number 55245 by Tawa1 last updated on 20/Feb/19

Answered by tanmay.chaudhury50@gmail.com last updated on 20/Feb/19

F_1 =9×10^9 ×((20×10)/3^2 ) F_2 =9×10^9 ×((16×10)/2^2 ) F_R =(√(F_1 ^2 +F_2 ^2 +2F_1 F_2 cos90^o )) =(√(F_1 ^2 +F_2 ^2 )) (√((9×10^9 ×((20×10)/3^2 ))^2 +(9×10^9 ×((16×10)/2^2 ))^2 )) =(9×10^9 ×10)^ ×(√(((400)/(81))+((256)/(16)))) =9×10^(10) ×(√(16+((400)/(81)))) =9×10^(10) ×(√(16(1+((25)/(81))))) =36×10^(10) ×1.14 =41.04×10^(10) N

$${F}_{\mathrm{1}} =\mathrm{9}×\mathrm{10}^{\mathrm{9}} ×\frac{\mathrm{20}×\mathrm{10}}{\mathrm{3}^{\mathrm{2}} } \\ $$$${F}_{\mathrm{2}} =\mathrm{9}×\mathrm{10}^{\mathrm{9}} ×\frac{\mathrm{16}×\mathrm{10}}{\mathrm{2}^{\mathrm{2}} } \\ $$$${F}_{{R}} =\sqrt{{F}_{\mathrm{1}} ^{\mathrm{2}} +{F}_{\mathrm{2}} ^{\mathrm{2}} +\mathrm{2}{F}_{\mathrm{1}} {F}_{\mathrm{2}} {cos}\mathrm{90}^{{o}} }\:=\sqrt{{F}_{\mathrm{1}} ^{\mathrm{2}} +{F}_{\mathrm{2}} ^{\mathrm{2}} }\: \\ $$$$\sqrt{\left(\mathrm{9}×\mathrm{10}^{\mathrm{9}} ×\frac{\mathrm{20}×\mathrm{10}}{\mathrm{3}^{\mathrm{2}} }\right)^{\mathrm{2}} +\left(\mathrm{9}×\mathrm{10}^{\mathrm{9}} ×\frac{\mathrm{16}×\mathrm{10}}{\mathrm{2}^{\mathrm{2}} }\right)^{\mathrm{2}} }\: \\ $$$$=\left(\mathrm{9}×\mathrm{10}^{\mathrm{9}} ×\mathrm{10}\right)^{} ×\sqrt{\frac{\mathrm{400}}{\mathrm{81}}+\frac{\mathrm{256}}{\mathrm{16}}}\: \\ $$$$=\mathrm{9}×\mathrm{10}^{\mathrm{10}} ×\sqrt{\mathrm{16}+\frac{\mathrm{400}}{\mathrm{81}}}\: \\ $$$$=\mathrm{9}×\mathrm{10}^{\mathrm{10}} ×\sqrt{\mathrm{16}\left(\mathrm{1}+\frac{\mathrm{25}}{\mathrm{81}}\right)}\: \\ $$$$=\mathrm{36}×\mathrm{10}^{\mathrm{10}} ×\mathrm{1}.\mathrm{14} \\ $$$$=\mathrm{41}.\mathrm{04}×\mathrm{10}^{\mathrm{10}} {N} \\ $$

Commented by Tawa1 last updated on 20/Feb/19

God bless you sir. But sir, the value of F_R very wide. Hope the answer will be right. i used your formular and got, 411825205639.48001

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$$$\mathrm{But}\:\mathrm{sir},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{F}_{\mathrm{R}} \:\mathrm{very}\:\mathrm{wide}.\:\:\mathrm{Hope}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{will}\:\mathrm{be}\:\mathrm{right}. \\ $$$$\mathrm{i}\:\mathrm{used}\:\mathrm{your}\:\mathrm{formular}\:\mathrm{and}\:\mathrm{got},\:\:\:\:\:\:\mathrm{411825205639}.\mathrm{48001}\:\: \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 20/Feb/19