[別館]球面倶楽部零八式markIISR

東大入試数学中心。解説なので解答としては不十分。出題年度で並ぶようにしている。大人の解法やうまい解法は極めて主観的に決めている。

1915年(大正4年)東京帝國大學工科大學(數學1問)

[1](物理學)Explain the following terms:---
1. Potential energy.
2. Heat energy.
3. Electro-magnetic induction.

[2](化學)Classify the sugers and give their chief properties.

[3](数学)A circular cylindrical tank with flat ends and made of steel plates of uniform thickness throughout is to be constructed in such a way that its weight should be a minimum for a given volume. Find the ratio of its diameter to length.

[4](力學)A ship going at 20 knots along a circular path changes its direction from due north to North-west in two minutes: what is the radius of its path?

One knot = 6080 feet per hour.

[5](力學)A heavy particle is suspended from a fixed point by a string of length a. A hrizontal velocity v_0 is suddenly inparted to the particle at rest at its lowest position, so that it begins to move in a vertical circle. Derive the expression for the velocity v_0 that makes the particle describe the whole circle.

[6](語學)Translate the following into English:---
Eine alte Kirche, welche den Sperlingen unzählige Nester gab, ward ausgebessert. Als sie nun in ihrem neuen Glanze da stand, kamen die Sperlinge wieder, ihre alten Wohnungen zu suchen. Allein sie fanden sie alle vermaurt. Zu was schrieen sie, taugt denn nun das große Gebäude? Kommt, verlaßt den unbrauchbaren Steinhaufen !

[6] Gotthold Ephraim Lessing, Fabeln

1915年(大正4年)東京帝國大學工科大學-數學(全1問) - [別館]球面倶楽部零八式markIISR