[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。

1910年(明治43年)東京帝國大學工科大學(數學2問)

[1] (物理學)A short iron bar tube having one end sealed weights 2 kilogrammes and contains air of 3 litres and of ordinary temperature and pressure. The tube is made of to sink into sea water at the same temperature. If the specific gravity of iron =7.8 and that of sea water =1.02, at what depth may the weights be removed and the tube just not ascent ?

[2] (物理學)Explain the following terms :---
Modulus of elasticity, Entropy, Electric potential, Radioactivity.

[3] Find the point of inflexion in the curve a^2y=3bx^2-x^3 and determine the curvature at the origin.

[4] The radius of the base of a right cone is 5 inches and the altitude of the cone is 5\sqrt{2} inches. Find the greatest parabolic section of the cone in square inches.

[5] (力學)A ball falling from the top of a tower had descended a feet when another was dropped at a distance b ft from the top of the tower and they reached the ground together. Find the height of the tower.

[6] (力學)Two uniform bars connected at a common extremity by a smooth joint, are placed in a vertical plane, their other extremities which rest on a smooth horizontal plane, being connected by a cord. Find the tension of the cord.

[7] (英語)Translate
a. 受驗者ハ其答案ニハ必ズ受驗番號ト問題番號トヲ記入スベシ。
b. 答案ハ一問題毎ニ別々ニ其答案受取所ニ差出スベシ。
c. 答案ナキ場合ト雖モ受驗番號ト問題番號トヲ記入シタル紙ヲ提出スベシ。

[8] (英語)Translate the following letter into English : ---
拜啓僕は豫テ工科大學ニ於テ電氣工學科ヲ收ムル希望ヲ抱キ居リ候處該科志望者ハ御承知ノ如ク遙カニ豫定人員ニ超過セシヲ以テ本月十五日競爭試驗ヲ受候處幸ニシテ第一席ニ及第者トシテ入學シ得ルコトニ相成リ申シ候右ノ次第ニ候間御安神被下度候 早々頓首

1910年(明治43年)東京帝國大學工科大學-數學[3] - [別館]球面倶楽部零八式markIISR
1910年(明治43年)東京帝國大學工科大學-數學[4] - [別館]球面倶楽部零八式markIISR

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