1914年(大正3年)東京帝國大學工科大學(數學1問) - [別館]球面倶楽部零八式markIISR

[1]（物理學）A quantity of air at atomosphereic pressure is compressed so tha its volume is reduced to one-tenth, the temperature being raised from $23^{\circ}\mbox{C}$ to $37^{\circ}\mbox{C}$ : express the new pressure in atomospheres.

[2]（化學）Explain what are meant by the following terms :---
a. The thermal dissociation.
b. The electrolytic dissociation.

[3]（数学）From $\mbox{F}$ one of the foci of a given ellipse, radius vectors are drawn dividing the angle $\mbox{AFB}=\pi$ into $n$ equal parts, $\mbox{AB}$ being the major axis of the ellipse. Find the arithmetrical mean of these radius vectores when $n=\infty$ .

[4]（力學）A ship of 20000 tons weight moving with a velocity of one foot per second collides against a sand bank and is stepped in 3 seconds. What is the average force during the collision?

[5]（力學） $\mbox{ABCD}$ is a square lamina of uniform density; $\mbox{E},\mbox{F}$ are the middle points of $\mbox{AB}$ and $\mbox{BC}$ ; if the corner of the square is folded along the line $\mbox{EF}$ (so that $\mbox{B}$ comes on to the center of the square); find the center of gravity of the lamina under the new circumstances.