Question

Unit of length mass and time independent with each other

Answer 1

It turns out that they are not, provided we choose a different ‘coordinate system of units', which is the Planck system. The fundamental constants of nature are really c(maximal speed~speed of light),h(Planck’s constant)and G(Newton's gravitational constant). Length, mass and time are some derived notions which we use!Taking into consideration relativity and quantum mechanics allows us to choose c=h=1(Planck units) and hence

E=M;l=T;E=1l. (Using E=Mc2 and E=hν)

=>l=T=1M

Where E: Energy, M: Mass, L: Length, T: Time

Answer 2

ᴀɴsᴡᴇʀ:

ᴀɴʏ ᴍᴇᴄʜᴀɴɪᴄᴀʟ ϙᴜᴀɴᴛɪᴛʏ ᴄᴀɴ ʙᴇ ᴇxᴘʀᴇssᴇᴅ ɪɴ ᴛᴇʀᴍs ᴏғ ᴛʜʀᴇᴇ ғᴜɴᴅᴀᴍᴇɴᴛᴀʟ ϙᴜᴀɴᴛɪᴛɪᴇs, ᴍᴀss, ʟᴇɴɢᴛʜ ᴀɴᴅ ᴛɪᴍᴇ. ғᴏʀ ᴇxᴀᴍᴘʟᴇ, sᴘᴇᴇᴅ ɪs ᴀ ʟᴇɴɢᴛʜ ᴅɪᴠɪᴅᴇᴅ ʙʏ ᴛɪᴍᴇ. ғᴏʀᴄᴇ ɪs ᴍᴀss ᴛɪᴍᴇs ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ, ᴀɴᴅ ɪs ᴛʜᴇʀᴇғᴏʀᴇ ᴀ ᴍᴀss ᴛɪᴍᴇs ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴅɪᴠɪᴅᴇᴅ ʙʏ ᴛʜᴇ sϙᴜᴀʀᴇ ᴏғ ᴀ ᴛɪᴍᴇ .