Question

On a stretched string, the frequency of vibration is given by f = (1/2 L) (T/m). In this equation, m has the dimension:

Options

A
ML^-2
B
ML^-1
C
M
D
ML

Explanation

In this equation, 'm' represents mass per unit length, so the correct dimension is [ML^‐1]

Incorrect as per formula

To determine the dimensions of the variable "m" in the equation f = (1/2L) / √(T/m), we can analyze the dimensions of each term involved.

Frequency (f): Frequency is measured in units of 1/time, typically hertz (Hz), which is equal to 1/second (s^-1).

Length (L): Length is measured in units of distance, such as meters (m).

Tension (T): Tension is measured in units of force, such as newtons (N).

Mass (m): Mass is measured in units of mass, such as kilograms (kg).

Using the principle of dimensional analysis, we can equate the dimensions on both sides of the equation to find the dimensions of "m".

On the left-hand side, the dimension is 1/time (T).

On the right-hand side, we have (1/2L) / √(T/m), which simplifies to (1/(T(Tm.s-1(T1/2 L)) * (m/L). To equate dimensions, we need to cancel out the dimensions of (T) and L, leaving only the dimension of mass.

Therefore, the dimension of "m" is ML(-1), which means mass per unit length or mass divided by length.

Incorrect as per formula