UNIVERSAL GRAVITATION PRACTICE QUIZ

solutions

1.

The English physicist who first measured Gwas

a. Albert Einstein b. Isaac Newton

c. Charles Coulomb d. Henry Cavendish

2.

The Universal Gravitation Constant is described as

a. universal gravity b. the strength of gravity

c. distance behavior d. mass behavior

3.

True or False: The inverse square law states “If one quantity is multiplied by a factor, another quantity decreases by the square of that factor.”

𝑦 =1

𝑥2

𝐹 = 𝐺𝑚1𝑚2

𝑑2

INVERSE SQUARED LAW

𝑎 =1

𝑏2𝑖𝑓 𝑎 𝑖𝑠 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 x, 𝑡ℎ𝑒𝑛 𝑏 𝑖𝑠 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓

1

𝑥2.

𝑎 =1

𝑏2𝑖𝑓 𝑏 𝑖𝑠 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 x, 𝑡ℎ𝑒𝑛 𝑎 𝑖𝑠 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓

1

𝑥2.

𝑎 =1

𝑏2𝑖𝑓 𝑎 𝑖𝑠 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 x, 𝑡ℎ𝑒𝑛 𝑏 𝑖𝑠 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓

1

𝑥2.

𝑎 =1

𝑏2𝑖𝑓 𝑏 𝑖𝑠 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 x, 𝑡ℎ𝑒 𝑎 𝑖𝑠 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦 𝑎 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑓

1

𝑥2.

𝑒𝑥𝑎𝑚𝑝𝑙𝑒: 𝑖𝑓 𝑎 𝑖𝑠 𝑑𝑜𝑢𝑏𝑙𝑒𝑑, 𝑡ℎ𝑒𝑛 𝑏 𝑖𝑠 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑏𝑦1

22=

1

4.

𝑚𝑒𝑎𝑛𝑖𝑛𝑔 2𝑎 𝑤𝑖𝑙𝑙 𝑟𝑒𝑠𝑢𝑙𝑡 𝑖𝑛1

4𝑏

4.

Knowing that the universal gravitational force is given by the equation

𝐹 = 𝐺𝑚1𝑚2

𝑑2if one of the mass is doubled and the distance is also double, how

does this change the force?

a. The force would double. b. The force would be halved.

c. The force would be the same. d. The force would quadruple.

𝐹𝑜𝑙𝑑 = 𝐺𝑚1𝑚2

𝑑2𝐹𝑛𝑒𝑤 = 𝐺

2𝑚1𝑚2

(2𝑑)2= 𝐺

2𝑚1𝑚2

4𝑑2=

1

2𝐺

𝑚1𝑚2

𝑑2=

1

2𝐹𝑜𝑙𝑑

5.

Which of the following is the correct value for G?

a. 6.67 x 1011 m3 kg/s2 b. 6.67 x 10-11 m3/(kg s2)

c. 6.76 x 10-11 N /m2 kg d. 6.76 x 1011 m3/(kg s2)

6.

What is your weight at the center of the Earth?

a. the same as it was at the surface of the Earth.

b. twice the weight at the surface of the Earth.

c. half the weight at the surface of the Earth.

d. zero

7.

If you are standing on a scale in an elevator and it was accelerating downward,

your weight would be

a. greater than your normal weight.

b. equal to your normal weight.

c. less than your normal weight.

8.

What is used to explain the tides of the oceans?

a. Earth’s acceleration around the sun.

b. The pulls of the other planets.

c. Sun and Moon gravitational pulls on Earth.

d. Earth’s gravity.

9.

True or False. When the sun runs out of fusion fuel, Helium, gravitation will dominate, and the sun will start to collapse.

hydrogen

10.

A small light source located 1 m in front of an

opening of area 1 m2 illuminates a wall behind. If

the wall is 1 m behind the opening (2 m from the

light source), the illuminated area covers 4 m2.

How many square meters will be illuminated if the wall is

8 meters from the source?

𝑎𝑟𝑒𝑎 = 𝑡ℎ𝑒 𝑠𝑞𝑢𝑎𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 82 = 64𝑚2

a. 4 m2 b. 16 m2 c. 64 m2 d. 100 m2

11.

Consider a planet of uniform density that has a straight tunnel from the North Pole

through the center to the South Pole. At the surface of the planet, an object weighs

1 ton. What is the weight of the object if it is 2/3 of the distance to the center of the

planet.

a. 2/3 tons b. 3/2 tons c. 4/9 tons d. 9/4 tons

2

3𝑡ℎ𝑒 𝑤𝑎𝑦 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑐𝑒𝑛𝑡𝑒𝑟 𝑖𝑠

2

3𝑜𝑓 𝑡ℎ𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛

2

3𝑜𝑓 𝑡ℎ𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑖𝑠

2

3𝑜𝑓 𝑡ℎ𝑒 𝑤𝑒𝑖𝑔ℎ𝑡.

12.

Knowing that the universal gravitational force is given by the equation

𝐹 = 𝐺𝑚1𝑚2

𝑑2, if both of the masses are doubled and the distance is also doubled,

how does this change the force?

a. The force is doubled. b. The force would be halved.

c. The force would stay the same. d. The force would quadrupled.

𝐹𝑜𝑙𝑑 = 𝐺𝑚1𝑚2

𝑑2𝐹𝑛𝑒𝑤 = 𝐺

2𝑚12𝑚2

(2𝑑)2= 𝐺

4𝑚1𝑚2

4𝑑2= 𝐺

𝑚1𝑚2

𝑑2= 𝐹𝑜𝑙𝑑

13.

Calculate the force between two objects that have masses of 70 kilograms and

2,000 kilograms separated by a distance of 1 meter.

a. 9.34 x 10-6 N b. 2.86 x 10-6 N

c. 4.67 x 10-6 N d. 5.72 x 10-6 N

𝐹 = 𝐺𝑚1𝑚2

𝑑2= 6.67 × 10−11

70 2000

12= 9.37 × 10−6𝑁

14.

Calculate the forces between the two spheres

as shown in the diagram.

a. 1.85 N b. 1.85 x 10-4 N

c. 2.6 x 104 N d. 2.22 x 10-7 N

𝐹 = 𝐺𝑚1𝑚2

𝑑2= 6.67 × 10−11

1000 1000

(0.3+0.3)2= 1.85 × 10−4𝑁

15.

A satellite is orbiting Earth at a distance of 35 kilometers. The satellite has a mass of 500 kilograms. What is the force between the planet and the satellite?

a. 2500 N b. 3203 N c. 4845 N d. 6234 N

𝐹 = 6.67 × 10−11(500)(5.9742×1024)

(6.378×106+35000)2= 4845 𝑁

16.

The mass of the sun is 1.99 x 1030 kilograms and its distance from Earth is 150 million kilometers (150 x 109 meters). What is the gravitational force between the sun and Earth?

a. 2.45 x 1025 N b. 2.72 x 1024 N

c. 8.42 x 1022 N d. 3.52 x1022 N

𝐹 = 𝐺𝑚1𝑚2

𝑑2= 6.67 × 10−11

1.99×1030 5.97×1024

(150×109)2= 3.52 × 1022𝑁

17.

If the gravitational force between objects of equal mass is 4.60x10‐8 N when the objects

are 100.0 m apart, what is the mass of each object?

a. 2626 kg b. 3242 kg

c. 1287 kg d. 2164 kg

𝐹 = 𝐺𝑚1𝑚2

𝑑2

4.60 × 10−8 = 6.67 × 10−11𝑚2

(100)2

4.60 × 10−8 = 6.67 × 10−15𝑚2

𝑚 =4.60×10−8

6.67×10−15= 2626 𝑘𝑔

18.

If two objects, each with a mass of 3.0x102 kg, produce a gravitational force

between them of 5.4 x10‐6 N. What is the distance between them?

a. 3.12 m b. 1.05 m

c. 4.81 m d. 2.68 m

𝐹 = 𝐺𝑚1𝑚2

𝑑2

5.4 × 10−6 = (6.67 × 10−11)(3.0×102)2

𝑑2

𝑑2 =6.67×10−11 (3.0×102)2

5.4×10−6𝑑 =

6.67×10−11 (3.0×102)2

5.4×10−6= 1.05 𝑚

19.

What is the gravitational force on a 150.0-kg object that is 5.25x107 m above the

Earth’s surface?

a. 17.0 N b. 21.4 N c. 150 N d. 32.8 N

𝐹 = 𝐺𝑚1𝑚2

𝑑2

𝐹 = 6.67 × 10−11(150)(5.97×1024)

((6.371×106)+(5.25×107))2

𝐹 = 17.02 𝑁

20.

True or False, a 1000-kg object placed exactly between the Moon and the Earth will eventually falls towards the Moon.