[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。

1911年(明治44年)東京帝國大學工科大學(數學1問)

[1] (物理學)A cubic meter of air is heated under the normal atomospheric pressure until its volume is doubled. How much of the heat supplied to it is converted into external work.

[2] (物理學)Explain how the velocity of sound in air varies when its temperature and pressure are changed.

[3] (化學)Explain fully what are meant by acids, bases and salts.

[4] (化學)Give the constitutional formula of all the alchols having a molecular formula \mbox{C}_4\mbox{H}_{10} and state their behaviors towards oxidising agents.

[5](數學)Find the locus of a point P fixed in a straight line AB of constant length which moves with its extremities A,B on two fixed straight lines, making an angle \alpha with each other. To what family of curves does the locus belong ?

[6] (力學)A weight \mbox{P} is kept at rest upon a smooth inclined plane by the tension of a weightless string passing over a frictionless pulley placed above the plane, the tension being produced by a weight ``a'' attached at the other end of the string and hanging freely. Find the position of equilibium and the corresponding reaction of the plane.

[7] (英語)Write a letter in English to a friend inducing him to learn swimming, the skeleton of the letter being as follows : ---
Swimming a neccessary part of education ; useful in saving life ; develpos the muscle ; not difficult if learnt when young ; confidence and perseverance required.
State how when and where you learnt to swim ; how long it took you to learn ; describe the pleasure and feeling that you obtain from the exercise.

[8] (英語)Translate the following passages into English : ---
無線電信は現今千哩以上通信確實となりたれども遠距離の無線電話が好成績を收めたる實例は未だ聞かず然るに最近佛國海軍は地中海に於て二隻の軍艦上に一種の無線電話機を裝置し海上六十五哩の距離に於て通話を試み遂に成行せりと云ふ。

1911年(明治44年)東京帝國大學工科大學-數學[5] - [別館]球面倶楽部零八式markIISR