Question

20£®¾Ý±¨µÀ£¬2020ÄêÇ°ÎÒ¹ú½«·¢Éä8¿Åº£ÑóϵÁÐÎÀÐÇ£¬°üÀ¨4¿Åº£ÑóˮɫÎÀÐÇ£¬2¿Åº£Ñó¶¯Á¦»·¾³ÎÀÐǺÍ2¿Åº£Â½À×´ïÎÀÐÇ£¬ÒÔ¼ÓÇ¿¶Ô»ÆÑÒµº¡¢µöÓ㵺¼°Î÷ɳȺµºÈ«²¿µºÓ츽½üº£ÓòµÄ¼à²â£®É躣½À×´ïÎÀÐÇÈƵØÇò×öÔÈËÙÔ²ÖÜÔ˶¯µÄ¹ìµÀ°ë¾¶ÊǺ£Ñó¶¯Á¦»·¾³ÎÀÐǵÄn±¶£¬ÏÂÁÐ˵·¨ÕýÈ·µÄÊÇ£¨¡¡¡¡£©

• A£® ÔÚÏàͬʱ¼äÄÚ£¬º£Â½À×´ïÎÀÐǵ½µØÐĵÄÁ¬Ïßɨ¹ýµÄÃæ»ýÓ뺣Ñó¶¯Á¦»·¾³ÎÀÐǵ½µØÐĵÄÁ¬Ïßɨ¹ýµÄÃæ»ýÏàµÈ
• B£® ÔÚÏàͬʱ¼äÄÚ£¬º£Â½À×´ïÎÀÐǵ½µØÐĵÄÁ¬Ïßɨ¹ýµÄÃæ»ýÓ뺣Ñó¶¯Á¦»·¾³ÎÀÐǵ½µØÐĵÄÁ¬Ïßɨ¹ýµÄÃæ»ýÖ®±ÈΪ$\sqrt{n}$£ºl
• C£® º£Â½À×´ïÎÀÐÇÓ뺣Ñó¶¯Á¦»·¾³ÎÀÐÇÏßËÙ¶ÈÖ®±ÈΪ$\sqrt{n}$£ºl
• D£® º£Â½À×´ïÎÀÐÇÓ뺣Ñó¶¯Á¦»·¾³ÎÀÐÇÏòÐļÓËÙ¶ÈÖ®±ÈΪ n²£º1

Answer 1

·ÖÎö ÍòÓÐÒýÁ¦ÌṩÏòÐÄÁ¦£¬¸ù¾ÝÍòÓÐÒýÁ¦¶¨ÂɺÍÅ£¶ÙµÚ¶þ¶¨ÂÉÁÐʽ±È½ÏÏßËٶȡ¢ÖÜÆÚ¡¢ÏòÐļÓËٶȵĴóСµÄ±í´ïʽ£¬ÓÉ´Ë¿ÉÒÔÅжϸ÷¸öÑ¡Ïî

½â´ð ½â£ºÓÉÍòÓÐÒýÁ¦ÌṩÏòÐÄÁ¦£º$G\frac{Mm}{{r}^{2}}$=mr¦Ø²=m$\frac{{v}^{2}}{r}$=ma   ¿ÉµÃ$¦Ø=\sqrt{\frac{GM}{{r}^{3}}}$£¬v=$\sqrt{\frac{GM}{r}}$  a=$\frac{GM}{{r}^{2}}$
AB¡¢ÎÀÐǵ½µØÐĵÄÁ¬Ïßɨ¹ýµÄÃæ»ýΪS=$\frac{¦Øt}{2¦Ð}$¦Ðr²=$\frac{¦Øt}{2}{r}^{2}$=$\frac{\sqrt{GMr}}{2}$t£¬ÔòA´íÎó£¬BÕýÈ·
C¡¢ÓÉ v=$\sqrt{\frac{GM}{r}}$ ¿ÉµÃº£Â½À×´ïÎÀÐÇÓ뺣Ñó¶¯Á¦»·¾³ÎÀÐÇÏßËÙ¶ÈÖ®±ÈΪ1£º$\sqrt{n}$£¬ÔòC´íÎó
D¡¢ÓÉ  a=$\frac{GM}{{r}^{2}}$¿ÉµÃº£Â½À×´ïÎÀÐÇÓ뺣Ñó¶¯Á¦»·¾³ÎÀÐÇÏòÐļÓËÙ¶ÈÖ®±ÈΪ 1£ºn²ÔòD´íÎó
¹ÊÑ¡£ºB

µãÆÀ ¾ö±¾ÌâµÄ¹Ø¼üÕÆÎÕÍòÓÐÒýÁ¦ÌṩÏòÐÄÁ¦ÕâÒ»ÀíÂÛ£¬²¢Äܸù¾ÝÌâÒâ½áºÏÏòÐÄÁ¦µÄ¼¸ÖÖ²»Í¬µÄ±í´ïÐÎʽ£¬Ñ¡ÔñÇ¡µ±µÄÏòÐÄÁ¦µÄ±í´ïʽ£®