· 

2022京大Ⅰ

■解答

(ア) \(MV\)  (イ) \(\displaystyle\frac{1}{2}mv'^2+\frac{1}{2}MV^2\)  (ウ) \(\displaystyle\frac{M+m}{2m}V\)

(エ) \(\displaystyle\frac{M-m}{2m}V\)  (オ) \(M>m\)  (カ) \(\displaystyle\frac{M-m}{2m}\sqrt{\frac{2R}{g}}V\)

(キ) \(\sqrt{2gR}\)  (ク) \(M=3m\)

(ケ) \(\sqrt{gR\cos\theta}\)  (コ) \(\sqrt{gR(2+3\cos\theta)}\)  (サ) \(\displaystyle\frac{1}{2}\sqrt{\frac{gR}{2}}\)

(シ) \(\displaystyle\frac{3}{2}\sqrt{\frac{3gR}{2}}\)  (ス) \(\displaystyle\frac{V_1}{g}(V_2+\sqrt{V_2^2+2gR})\)

■解説