Question

Find the dimension of the velocity
gradient.​

Answer 1

Explanation:

Velocity Gradient V is defined as rate of change in velocity per unit of distance. Mathematically, Velocity Gradient= velocity/distance.

Dimensionally V=

[L]

[M

0

L

1

T

−1

]

=[M

0

L

0

T

−1

]

Answer 2

Dimensionally V=[L][M0L1T−1]=[M0L0T−1]

Explanation:

ᴡᴇ ᴄᴀɴ ᴀʟsᴏ sᴀʏ ᴛʜᴀᴛ ᴠᴇʟᴏᴄɪᴛʏ ɢʀᴀᴅɪᴇɴᴛ ɪs ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴠᴇʟᴏᴄɪᴛʏ ᴘᴇʀ ᴜɴɪᴛ ᴅɪsᴛᴀɴᴄᴇ. ɴᴏᴡ ᴡᴇ ᴄᴀɴ ᴡʀɪᴛᴇ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ғᴏʀᴍᴜʟᴀs ғᴏʀ ᴇᴀᴄʜ ǫᴜᴀɴᴛɪᴛʏ. ᴅɪᴍᴇɴsɪᴏɴᴀʟ ғᴏʀᴍᴜʟᴀ ғᴏʀ ᴠᴇʟᴏᴄɪᴛʏ ɪs [ʟᴛ−] ʙᴇᴄᴀᴜsᴇ ᴠᴇʟᴏᴄɪᴛʏ ɪs ᴅᴇғɪɴᴇᴅ ᴀs ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴅɪsᴛᴀɴᴄᴇ ᴡɪᴛʜ ᴛɪᴍᴇ.