1912年(明治45年)東京帝國大學工科大學(數學2問) - [別館]球面倶楽部零八式markIISR

[1] （物理學）An object at a distance of 2 inches from a convex lens has its image magnified three times. What is the focal length of the lens?

[2] （物理學）What different phenomena would be observed if the following substances be braught one at a time near a pole of a bar-magnet in air?
a. A piece of soft iron.
b. A piece of steel.
c. A piece of zinc.
d. A piece of nickel.
e. A piece of bismuth.
f. A piece of copper wire carrying electric current.
g. A small magnetic needle.

[3] （化學）Explain the catalysis and the hydrolysis with practical examples.

[4]（數學）The equation to the curve is $y=b\left\{1-\left(\dfrac{x}{l}\right)^m\right\}$ . Find the value of $m$ that makes the area $\rm OACB$ equal to $\dfrac{2}{3}bl$ .
(圖省略)

[5]（數學）The altitude of a circular cone is 100 inches and decreasing at the rate of 10 inches per second ; and radius of the base is 50 inches and increasing at the rate of 5 inches per second. At what rate is the volume changing ?

[6]（力學）A gun, of mass $M$ , with its barrel horizontal fires a shot of mass $m$ ; when the gun is fixed, the shot strikes a point $\mbox{A}$ on a vertical wall in front of the gun at a depth $h$ below the barrel. Prove that, if the gun be free to move on a horizontal plane, the shot will strike the wall at a point $\mbox{B}$ which lies below the point $\mbox{A}$ by $\dfrac{mh}{M}$ .
圖省略