Question

question 20
the diagram below shows five objects in space. object 1 is at equal distance from object 2, object 3, object 4, and object 5.
the mass of object 2 is double the mass of object 5. the mass of object 4 is half of the mass of object 5 and the mass of object 3 is half of the mass of object 4.
which of these objects attracts object 1 with the least gravitational force?
object 1
object 2
object 3
object 4

Explanation:

Step1: Recall gravitational - force formula

The gravitational - force formula is $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them. Since the distance $r$ from Object 1 to Object 2, Object 3, Object 4, and Object 5 is the same, the gravitational force is directly proportional to the product of the mass of Object 1 and the mass of the other object. Let the mass of Object 5 be $m$.

Step2: Express masses of other objects in terms of $m$

The mass of Object 2 is $2m$ (because the mass of Object 2 is double the mass of Object 5). The mass of Object 4 is $\frac{m}{2}$ (since the mass of Object 4 is half of the mass of Object 5), and the mass of Object 3 is $\frac{1}{2}\times\frac{m}{2}=\frac{m}{4}$ (as the mass of Object 3 is half of the mass of Object 4).

Step3: Compare the masses

We compare the masses of Object 2 ($2m$), Object 3 ($\frac{m}{4}$), Object 4 ($\frac{m}{2}$), and Object 5 ($m$). Among these values, $\frac{m}{4}$ (mass of Object 3) is the smallest.

Answer:

Object 3