Question

Derive the relationship between 'g' and 'G'
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Answer 1

Answer:

g = G*M/R^2, is the relationship between g and G

Answer 2

$\Huge\bold\green{Qᴜᴇꜱᴛɪᴏɴ?:}$

Derive the relationship between 'g' and 'G'

$\Huge\bold\red{ᴀɴꜱᴡᴇʀ:}$

ɢ' & ‘ɢ' ᴀʀᴇ ʀᴇʟᴀᴛᴇᴅ ᴛᴏ ɢʀᴀᴠɪᴛᴀᴛɪᴏɴᴀʟ ꜰᴏʀᴄᴇ.

ɢ ɪꜱ ᴋɴᴏᴡɴ ᴀꜱ ᴜɴɪᴠᴇʀꜱᴀʟ ɢʀᴀᴠɪᴛᴀᴛɪᴏɴᴀʟ ᴄᴏɴꜱᴛᴀɴᴛ. ɪᴛꜱ ɴᴜᴍᴇʀɪᴄᴀʟ ᴠᴀʟᴜᴇ ɪꜱ 6.67 × 10^-11 ɴ-ᴍ²/ᴋɢ²

ɢ ɪꜱ ᴋɴᴏᴡɴ ᴀꜱ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴅᴜᴇ ᴛᴏ ɢʀᴀᴠɪᴛʏ. ᴀɴᴅ ɪᴛꜱ ɢᴇɴᴇʀᴀʟʟʏ ɴᴜᴍᴇʀɪᴄᴀʟ ᴠᴀʟᴜᴇ ɪꜱ 9.8 ᴍ/ꜱ². ɪᴛ ɪꜱ ᴄʜᴀɴɢᴇᴀʙʟᴇ. ɪᴛ ɪꜱ ᴅɪꜰꜰᴇʀᴇɴᴛ ꜰᴏʀ ᴘʟᴀᴄᴇ ɪɴ ᴇᴀʀᴛʜ. ɢ = 10 ᴍ/ꜱ² ɪɴ ᴘᴏʟᴇꜱ.

ᴛʜᴇ ʀᴇʟᴀᴛɪᴏɴ ʙᴇᴛᴡᴇᴇɴ ‘ɢ’ & ‘ɢ' :-

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛʜᴇ ɴᴇᴡᴛᴏɴ’ꜱ ʟᴀᴡ ᴏꜰ ɢʀᴀᴠɪᴛᴀᴛɪᴏɴ -

ꜰ = ɢ ᴍ.ᴍ / ʀ² -(ɪ)

ᴡʜᴇʀᴇ ᴍ ᴀɴᴅ ᴍ ᴀʀᴇ ᴛᴡᴏ ᴍᴀꜱꜱᴇꜱ ᴅɪꜱᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ʀ ᴍᴇᴛʀᴇ.

ʙʏ ɴᴇᴡᴛᴏɴ'ꜱ ꜱᴇᴄᴏɴᴅ ʟᴀᴡ :-

ꜰ = ᴍɢ -(ɪɪ)

ᴡʜᴇʀᴇ ꜰ ɪꜱ ꜰᴏʀᴄᴇ ᴀɴᴅ ᴍ ɪꜱ ᴍᴀꜱꜱ ᴀɴᴅ ɢ ɪꜱ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴅᴜᴇ ᴛᴏ ɢʀᴀᴠɪᴛʏ.

ɴᴏᴡ ᴇQᴜᴀᴛɪɴɢ ᴇQᴜᴀᴛɪᴏɴ (ɪ) ᴀɴᴅ (ɪɪ) ᴛʜᴀɴ:-

= ᴍɢ = ɢ ᴍ.ᴍ / ʀ²

= ɢ = ɢ ᴍ / ʀ² -(ɪɪɪ)

ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇQᴜ. (ɪɪɪ) ɪꜱ ᴛʜᴇ ʀᴇʟᴀᴛɪᴏɴ ʙᴇᴛᴡᴇᴇɴ ‘ɢ’ ᴀɴᴅ ‘ɢ'.

Thank you✌️❣️✌️