Question

7£®Í¨¹ý¹Û²â·¢ÏÖijÐÇÇò°ë¾¶ÊǵØÇò°ë¾¶µÄk±¶£¬ÈƸÃÐÇÇò½üµØÔËÐÐÎÀÐǵÄÖÜÆÚÊǵØÇò½üµØÎÀÐÇÖÜÆÚµÄn±¶£¬ÏÂÁÐ˵·¨ÖдíÎóµÄÊÇ£¨¡¡¡¡£©

• A£® ÈƸÃÐÇÇò½üµØÔËÐÐÎÀÐǵÄËÙ¶ÈÊǵØÇò½üµØÎÀÐÇËٶȵÄ$\frac{k}{n}$
• B£® ¸ÃÐÇÇòµÄÖÊÁ¿ÊǵØÇòÖÊÁ¿µÄ$\frac{{k}^{3}}{{n}^{2}}$
• C£® ¸ÃÐÇÇò±íÃæµÄÖØÁ¦¼ÓËÙ¶ÈÊǵØÇò±íÃæµÄÖØÁ¦¼ÓËٶȵÄ$\frac{k}{{n}^{2}}$
• D£® ¸ÃÐÇÇòµÄÃܶÈÊǵØÇòÃܶȵÄ$\frac{k}{{n}^{2}}$

Answer 1

·ÖÎö A¡¢¸ù¾Ýv=$\frac{2¦ÐR}{T}$±È½ÏÏßËٶȣ»
B¡¢¸ù¾ÝÍòÓÐÒýÁ¦µÈÓÚÏòÐÄÁ¦ÁÐʽÇó½â³öÖÊÁ¿µÄ±í´ïʽ½øÐзÖÎö£»
C¡¢¸ù¾Ýa=$\frac{4{¦Ð}^{2}}{{T}^{2}}r$Çó½âÎÀÐǵÄÏòÐļÓËٶȣ¬¼´ÎªÐÇÇò±íÃæµÄÖØÁ¦¼ÓËٶȣ»
D¡¢ÔÚBÏîÖÐÇó½â³öÁËÖÊÁ¿±È£¬¸ù¾Ý¹«Ê½$¦Ñ=\frac{M}{V}$È·¶¨ÐÇÇòµÄÃܶÈÖ®±È£®

½â´ð ½â£ºA¡¢¸ù¾Ýv=$\frac{2¦ÐR}{T}$£¬ÓУº
$\frac{{v}_{1}}{{v}_{2}}=\frac{{R}_{1}}{{R}_{2}}•\frac{{T}_{2}}{{T}_{1}}=k•\frac{1}{n}=\frac{k}{n}$
¹ÊAÕýÈ·£»
B¡¢ÎÀÐǵÄÍòÓÐÒýÁ¦µÈÓÚÏòÐÄÁ¦£¬¹Ê£º
$G\frac{Mm}{{R}^{2}}=m\frac{4{¦Ð}^{2}}{{T}^{2}}R$ 
½âµÃ£º
M=$\frac{4{¦Ð}^{2}{R}^{3}}{G{T}^{2}}$
¹Ê$\frac{{M}_{1}}{{M}_{2}}=£¨\frac{{R}_{1}}{{R}_{2}}£©^{3}£¨\frac{{T}_{2}}{{T}_{1}}£©^{2}={k}^{3}£¨\frac{1}{n}£©^{2}$=$\frac{{k}^{3}}{{n}^{2}}$
¹ÊBÕýÈ·£»
C¡¢ÓÉÓÚÊǽüµØÎÀÐÇ£¬¹ÊÐÇÇò±íÃæµÄÖØÁ¦¼ÓËٶȵÈÓÚÎÀÐǵÄÏòÐļÓËٶȣ¬Îª£ºa=$\frac{4{¦Ð}^{2}}{{T}^{2}}r$£»
¹Ê$\frac{{a}_{1}}{{a}_{2}}=£¨\frac{{T}_{2}}{{T}_{1}}£©^{2}\frac{{R}_{1}}{{R}_{2}}=£¨\frac{1}{n}£©^{2}k$=$\frac{k}{{n}^{2}}$
¹ÊCÕýÈ·£»
D¡¢ÔÚBÏîÖÐÇó½â³öÁËÖÊÁ¿±ÈΪ$\frac{{k}^{3}}{{n}^{2}}$£»
ÃܶÈΪ£º¦Ñ=$\frac{M}{V}=\frac{M}{\frac{4}{3}¦Ð{R}^{3}}$£»
¹Ê$\frac{{¦Ñ}_{1}}{{¦Ñ}_{2}}=\frac{{M}_{1}}{{M}_{2}}£¨\frac{{R}_{2}}{{R}_{1}}£©^{3}$=$\frac{{k}^{3}}{{n}^{2}}$•$£¨\frac{1}{k}£©^{3}$=$\frac{1}{{n}^{2}}$
¹ÊD´íÎó£»
±¾ÌâÑ¡´íÎóµÄ£¬¹ÊÑ¡£ºD

µãÆÀ ±¾Ì⿼²éÁËÈËÔìÎÀÐÇÎÊÌ⣬¹Ø¼üÊÇÃ÷È·ÎÀÐǵÄÍòÓÐÒýÁ¦µÈÓÚÏòÐÄÁ¦£¬¸ù¾ÝÅ£¶ÙµÚ¶þ¶¨ÂÉÁÐʽÖðÏî·ÖÎö£¬²»ÄÑ£®