I have to make sample questions for class

[PhysWiz3.14]

Can someone look these over and answer them so I can make sure my work is correct

1. The value of g at the Earth's surface is about 10 m/s2. What is its value at a distance from the Earth's center that is three times the Earth's radius?

2.Calculate the speed in meters per second at which the Earth revolves around the Sun. Assume the orbit is nearly circular, with radius r=1.5 10^11 m.

3. Somewhere between the Earth and the Moon, the gravitational pull exerted by these two bodies on a space pod would cancel. Is this location nearer the Earth or nearer the Moon?
A) Nearer the Earth.
B) Nearer the Moon.
C) At the half-way point.

Thanks for the help in advance.

 

[physixguru]

Welcome to PF.
FIRST ONE IS A BIT TOO LENGTHY.
SECOND ONE IS A GOOD ONE.
THIRD QUESTION DOES NOT IMPRESS ME MUCH.

 

[Moetasim]

1. The value of g decreases as we move away from the Earth's surface. Using the formula g=Gm/r^2, where G is the universal gravitational constant, m is the mass of the Earth, and r is the distance from the Earth's center, we can calculate the value of g at a distance that is three times the Earth's radius. Plugging in the values, we get g= (6.67x10^-11 Nm^2/kg^2)(5.97x10^24 kg)/(3(6.38x10^6 m))^2 = 2.22 m/s^2. Therefore, the value of g at a distance three times the Earth's radius is approximately 2.22 m/s^2.

2. The speed at which the Earth revolves around the Sun is given by the formula v=√(GM/r), where M is the mass of the Sun, r is the distance from the center of the Sun, and G is the universal gravitational constant. Plugging in the values, we get v=√((6.67x10^-11 Nm^2/kg^2)(1.99x10^30 kg)/ (1.5x10^11 m)) = 2.98x10^4 m/s. Therefore, the speed at which the Earth revolves around the Sun is approximately 29,800 m/s.

3. The location where the gravitational pull of the Earth and the Moon cancel out is known as the Lagrange point or the L1 point. This point is closer to the Moon than the Earth. Therefore, the answer is B) Nearer the Moon.