A space explorer lands on a certain planet and does an experiment to measure the local gravity. She launches an object straight upward and observes that it takes a total time T to return to the launch point and attains a maximum height h above the launch point. Derive an expression forthe value of g on this planet in terms of h and T and any appropriate constants.

Q: velocity of the proton in units of km/s

A: Given: Mass of proton is m=1.673×10-27 kg Charge on proton is q=1.6×10-19 C Radius of path is r=4.46…

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.