Question

state the conservation of momentum and prove it mathematically​

Answer 1

$\fbox\pink{A}\fbox\blue{n}\fbox\purple{s}\fbox\green{w}\fbox\red{e}\fbox\orange{r}$

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$\pink{❥}$ʟᴀᴡ ᴏғ ᴄᴏɴsᴇʀᴠᴀᴛɪᴏɴ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴛᴏᴛᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ sʏsᴛᴇᴍ ʀᴇᴍᴀɪɴs ᴄᴏɴsᴇʀᴠᴇᴅ ɪɴ ᴛʜᴇ ᴀʙsᴇɴᴄᴇ ᴏғ ᴇxᴛᴇʀɴᴀʟ ғᴏʀᴄᴇ.

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$\tt\blue{ᴘʀᴏᴏғ:}$

$\pink{❥}$Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.

$\tt\purple{★}$Let the two bodies remain in contact with each other for a small interval "delta t".

$\tt\purple{★}$Let F12 be the average force exerted by mass m1 on m2, and let F21 be the force on m2 due to m1.

$\tt\purple{★}$Let v1 and v2 be the velcoities of two bodies after collision.

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$\pink{❥}$ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴍᴀss ᴍ1 ʙᴇғᴏʀᴇ ᴄᴏʟʟɪsɪᴏɴ=ᴍ1ᴜ1

$\pink{❥}$ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴍᴀss ᴍ2 ᴀғᴛᴇʀ ᴄᴏʟʟɪsɪᴏɴ=ᴍ2ᴜ2

$\pink{❥}$ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴍᴀss ᴍ1 ᴀғᴛᴇʀ ᴄᴏʟʟɪsɪᴏɴ=ᴍ1ᴠ1

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$\pink{❥}$By using the definition of impulse, change in momentum of mass m1.

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♥️ᴍɪssᴀᴅᴏʀᴀʙʟᴇ♥️