Question

The

Two asteroids are 100,000 m apart. One has a mass of 3.5 x 106 kg. If
force of gravity between them is 1.05 x 104 N, what is the mass of the other
asteroid?
OA. 4.5 × 108 kg
OB. 4.5× 10⁹ kg
OC. 4.1 × 10⁹ kg
OD. 4.1 x 108 kg

Answer 1

Answer:The gravitational force between two masses can be calculated using Newton's law of universal gravitation:

�

=

�

⋅

�

1

⋅

�

2

�

2

F=

r

2

G⋅m

1

​

⋅m

2

​

​

Where:

�

F is the gravitational force (1.05 × 10^4 N)

�

G is the gravitational constant (

6.674

×

1

0

−

11

 

N

⋅

m

2

/

kg

2

6.674×10

−11

N⋅m

2

/kg

2

)

�

1

m

1

​

is the mass of one asteroid (3.5 × 10^6 kg)

�

2

m

2

​

is the mass of the other asteroid (unknown)

�

r is the distance between the asteroids (100,000 m)

First, rearrange the equation to solve for the mass of the second asteroid (

�

2

m

2

​

):

�

2

=

�

⋅

�

2

�

⋅

�

1

m

2

​

=

G⋅m

1

​

F⋅r

2

​

Now plug in the values:

�

2

=

1.05

×

1

0

4

 

N

⋅

(

100

,

000

 

m

)

2

6.674

×

1

0

−

11

 

N

⋅

m

2

/

kg

2

⋅

3.5

×

1

0

6

 

kg

m

2

​

=

6.674×10

−11

N⋅m

2

/kg

2

⋅3.5×10

6

kg

1.05×10

4

N⋅(100,000m)

2

​

Calculating this gives:

�

2

≈

4.5

×

1

0

9

 

kg

m

2

​

≈4.5×10

9

kg

So, the mass of the other asteroid is approximately

4.5

×

1

0

9

 

kg

4.5×10

9

kg, which matches option B:

4.5

×

1

0

9

 

kg

4.5×10

9

kg.

Answer 2

The answer is d 4.1 x 108 kg