The frequency upsilonof vibrations of uniform string of length l and stretched with a force F is given by upsilon = (p)/(2l)sqrt((F)/(m)) where p is the number of segments of the vibrating string and m is constant of the string. What is the dimensions of m?

The frequency upsilonof vibrations of uniform string of length l and s

1.	The frequency upsilonof vibrations of uniform string of length l and stretched with a force F is given by upsilon = (p)/(2l)sqrt((F)/(m)) where p is the number of segments of the vibrating string and m is constant of the string. What is the dimensions of m?
Answer» `[ML^(-1)T^(-1)]` `[ML^(-3)T^(0)]` `[ML^(-2)T^(0)]` `[ML^(-1)T^(0)]` Solution :Squaring both sides of the given relation, we get `upsilon^(2)= (p^(2))/(4l^(2))(F)/(m)` or `m= (p^(2)F)/(4l^(2)upsilon^(2))` `:.` dimensions of m `("dimensions of m")/("dimensions of" l^(2) xx "dimensions of" upsilon^(2))` (`:.` p is a DIMENSIONLESS QUANTITY) `=([MLT^(-2)])/([L^(2)][T^(-1)]^(2))= [ML^(-1)T^(0)]`