Question

Find the resultant gravitational force exerted on the object at the origin by the other two objects. The universal gravitational constant is 6.672 × 10−11 N · m2 /kg2 . Answer in units of N.

Answer 1

Answer:

The resultant gravitational force is $7.76\times10^{-11}\ N$

Explanation:

Suppose A coordinate system is constructed on the surface of a pool table, and three objects are placed on the coordinate system as follows: a 1.2 kg object at the origin, a 3 kg object at (0 m,1.8 m), and a 4.6 kg object at (4 m,0 m).

We need to calculate the gravitational force along x axis

Using formula of gravitational

$F_{1}=\dfrac{GmM}{r^2}$

Where, m = mass of first object

M = mass of object when placed at center

r = distance

G = gravitational constant

Put the value into the formula

$F_{1}=\dfrac{6.672\times10^{-11}\times1.2\times4.6}{(4)^2}$

$F_{1}=2.301\times10^{-11}\ N$

We need to calculate the gravitational force along y axis

Using formula of gravitational

$F_{2}=\dfrac{Gm_{1}M}{r^2}$

Put the value into the formula

$F_{2}=\dfrac{6.672\times10^{-11}\times1.2\times3}{(1.8)^2}$

$F_{2}=7.413\times10^{-11}\ N$

We need to calculate the resultant gravitational force

Using formula of resultant gravitational force

$F_{net}=\sqrt{(F_{1}^2+F_{2}^2)}$

$F_{net}=\sqrt{(2.301\times10^{-11})^2+(7.413\times10^{-11})^2}$

$F_{net}=7.76\times10^{-11}\ N$

Hence, The resultant gravitational force is $7.76\times10^{-11}\ N$