Question

Two masses, $800kg$ and $450kg$ are at a distance $25m$ apart. The magnitude of gravitational field intensity at a point $20m$ distant from the $800kg$ mass and $15m$ distant from the $450kg$ mass is $\sqrt{x}$ G (in N/kg). Then $x$ is $($where $G$ is universal gravitational constant$)$

• A. $6$
• B. $4$
• C. $7$
• D. $8$

Answer 1

The correct option is D $8$

Gravitational field due to $800kg=\frac{800G}{{20}^2}$

Gravitational field due to $400kg=\frac{450G}{{15}^2}$
${15}^2+{20}^2={25}^2$
So, the fields are also at right angles.
Resultant field $=\sqrt{{\left(\frac{800G}{{20}^2}\right)}^2+{\left(\frac{450G}{{15}^2}\right)}^2}$

$=G\sqrt{{\left(\frac{800}{400}\right)}^2+{\left(\frac{450}{225}\right)}^2}$
$=G\sqrt{8}$