Let g be the acceleration due to gravity at the surface of a planet of radius R. Which of the following is a dimensionally correct formula for the minimum kinetic energy K that a projectile of mass m must have at the planet's surface if the projectile is to escape from the planet's gravitational field?

A) K=sqt.(gR)
B) K=mgR
C) K=mg/R
D) K=m*sqt.(g/R)
E K=gR

(I thought the answer should be K=mgR/2, but the key is B)... )

The sum of all the extenral forces on a system of particles is zero. Which of the following must be true of the system?
A)the total mechanical energy is constant
B)total potential energy is constant
C)total kinetic energy is constant
D)total linear momentum is constant
E) it is in static equilibrium

I am so confused of these kind of question. How can I do these kind of problem? And when I see a problem, how can I figure out which method to use, momentum conservation or energy conservation, is easier? Is any characteristics?

Thanks!

Any helps??????????????
Please.............

Well, it seems like you're in a bit of a pickle. Don't worry, I'm here to help you out with a little bit of humor!

For the first question, imagine the planet as a pizza and the projectile as a slice that wants to escape. The minimum kinetic energy K the slice needs to have is proportional to its mass m and the planet's radius R. Now, let's analyze the answer choices:

A) K = sqrt(gR): It's like saying the slice needs to have the square root of a pizza to escape. Doesn't sound right, does it?

B) K = mgR: Now we're talking! This equation says that the slice needs to have its weight (mg) multiplied by the planet's radius (R) to escape the gravitational field. It's like saying the slice needs to have enough topping and crust to make a break for it. Brilliant!

C) K = mg/R: This equation is like saying the slice needs to be tiny (R in the denominator) to escape. Sorry, but size doesn't matter in this case.

D) K = m*sqrt(g/R): This one is a bit twisted. It's like saying the slice needs to have its mass multiplied by the square root of the radius divided by the gravitational acceleration. That's a recipe for confusion!

E) K = gR: Here it's saying that the slice needs to be the literal size of the gravitational acceleration times the radius. Well, that's just nonsense!

So, the correct answer is definitely B. The slice needs to have its weight multiplied by the planet's radius to escape. Who knew physics and pizza could go hand in hand?

Now, for your second question. When it comes to choosing between momentum conservation and energy conservation, you need to look at what's being asked in the problem. If they're asking about the motion of objects or forces involved, momentum conservation might be a good choice. But if they ask about work done, potential energy, or total energy, then energy conservation will come to the rescue.

Remember, when science gets tough, it's always good to have a sense of humor. Keep smiling and solving those problems!

To find the dimensionally correct formula for the minimum kinetic energy, you can use the principle of conservation of energy. The minimum kinetic energy required for a projectile to escape the planet's gravitational field is equal to the work done against gravity.

Let's analyze each option:

A) K = sqrt(gR)
This formula does not have the correct dimensions. The square root of a product (gR) does not match the dimensions of kinetic energy.

B) K = mgR
This formula does have the correct dimensions. The product of m (mass), g (acceleration due to gravity), and R (radius) matches the dimensions of kinetic energy (mass times distance squared per time squared).

C) K = mg/R
This formula does not have the correct dimensions. Dividing by R (distance) does not match the dimensions of kinetic energy.

D) K = m sqrt(g/R)
This formula does not have the correct dimensions. Taking the square root of a ratio (g/R) does not match the dimensions of kinetic energy.

E) K = gR
This formula does not have the correct dimensions. Multiplying g (acceleration due to gravity) by R (distance) does not match the dimensions of kinetic energy.

Therefore, the correct answer is B) K = mgR.