If the mass of the Earth were doubled but its radius remained the same, how would the acceleration due to gravity at the surface change?

Calculate the frequency of the travelling waves whose superposition gives this standing wave.

A meter stick lies on the bottom of a 100-cm-long tank with its zero mark against the left edge. You look into the tank at a 30°{“version”:”1.1″,”math”:”°”} angle, with your line of sight just grazing the upper left edge of the tank. What mark do you see on the meter stick if the tank is a) empty,  (3 marks) b) half full of water, and  (4 marks) c) completely full of water?  (3 marks)

A nerve cell is shaped like a cylinder. The membrane wall of the cylinder has a +0.07-V potential difference from the inside to the outside of the wall. To help maintain this potential difference, sodium ions with a charge of +e are pumped from inside the cell to the outside. For a typical cell, 109 ions are pumped each second.  (e=1.602×10-19 C) a.  How large is the surface of a nerve cell compared to a sodium ion?  Does the cell’s shape matter?  (2 marks) b.  Determine the change in chemical energy each second required to produce this increase in electric potential energy.  (4 marks) c.  If there are roughly 7×1011 of these cells in the body, how much chemical energy is used in pumping sodium ions each second?  (2 marks) d.  Estimate the fraction of a person’s metabolic rate used to pump these ions. Use 100 W as an average metabolic rate.  (2 marks)

Taking M⊙=2×1030 kg{“version”:”1.1″,”math”:”M⊙=2×1030 kg”} and R⊙=7×108 m{“version”:”1.1″,”math”:”R⊙=7×108 m”}, find the maximum deflection angle for light originating behind the sun observed during a solar eclipse. 

Taking M⊙=2×1030 kg{“version”:”1.1″,”math”:”M⊙=2×1030 kg”} and R⊙=7×108 m{“version”:”1.1″,”math”:”R⊙=7×108 m”}, find the maximum deflection angle for light originating behind the sun observed during a solar eclipse. 

Usually a source object will not lie on the axis determined by the observer and the deflecting mass. Which of the following are probable consequences of that asymmetric arrangement? I. In a dual-image lens effect, one image will show a time delay from the other. II. The effective index of refraction will differ significantly from its value for on-axis sources. III. An observed radio ring will appear thicker and brighter on one side than the other. 

Usually a source object will not lie on the axis determined by the observer and the deflecting mass. Which of the following are probable consequences of that asymmetric arrangement? I. In a dual-image lens effect, one image will show a time delay from the other. II. The effective index of refraction will differ significantly from its value for on-axis sources. III. An observed radio ring will appear thicker and brighter on one side than the other. 

Determine the effective focal length of a gravitational lens created by a celestial object of mass M0 and radius r0 assuming both that dS >> dL, so that rays coming from the source are parallel at the lens, and that tanθ≈θ{“version”:”1.1″,”math”:”tanθ≈θ”} (in radians) for small angles.

A train approaches a station at a constant speed, sounding its whistle continuously. Three students are discussing what an observer standing at a station would hear as the train is approaching. Which student is correct?