**Q3: **

A body moves along the -axis under the action of a force, . Given that , where m is the displacement from the origin, determine the work done on the body by when the body moves from to .

**Q4: **

**Q5: **

From Newtonβs universal gravitational law, we know that a body at a distance from the center of the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6371 km, find the magnitude of the work required for a satellite of mass 793 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.

- A 33β681β353.33 kg-wtβ km
- B 9β521β459.5 kg-wtβ km
- C 3β886β310 kg-wtβ km
- D 582β946.5 kg-wtβ km
- E 5β635β149.5 kg-wtβ km

**Q6: **

From Newtonβs universal gravitational law, we know that a body at a distance from the center of the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6371 km, find the magnitude of the work required for a satellite of mass 754 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.

- A 32β024β893.33 kg-wtβ km
- B 9β053β191 kg-wtβ km
- C 3β695β180 kg-wtβ km
- D 554β277 kg-wtβ km
- E 5β358β011 kg-wtβ km

**Q7: **

From Newtonβs universal gravitational law, we know that a body at a distance from the center of the Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of the Earth is 6371 km, find the magnitude of the work required for a satellite of mass 728 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.

- A 30β920β586.67 kg-wtβ km
- B 8β741β012 kg-wtβ km
- C 3β567β760 kg-wtβ km
- D 535β164 kg-wtβ km
- E 5β173β252 kg-wtβ km