Question

Masses of 1 kg, 2 kg and 3 kg are placed at the corners of an equilateral triangle of side 1m. The magnitude of the gravitational force exerted by 2 kg and 3 kg masses on the 1 kg mass is

• A. $\sqrt{17}G$
• B. $\sqrt{19}G$
• C. $\sqrt{15}G$
• D. $\sqrt{13}G$

Answer 1

Answer: (B)

$\sqrt{19}G$

$\theta ={60}^{\circ },F_1=\frac{2G}{1^2}=2G,F_2=\frac{3G}{1^2}=3G$
$F=\sqrt{F_1^2+F_2^2+2F_1{F}_{2}cos\theta }$
$F=\sqrt{(2G{)}^2+(3G{)}^2+2\left(2G\right)\left(3G\right)cos{60}^{\circ }}$
$F=G\sqrt{4+9+2\left(2\right)\left(3\right)\times \frac{1}{2}}$
$F=G\sqrt{4+9+6}$
$F=G\sqrt{19}$