Question

Given that the displacement of a particle is given by x = A sin^2 (Kt), where t denotes the time. The
unit of K is
(A) hertz
(B) metre
(C) radian
(D) second​

Answer 1

The unit of K is A.Hertz

Displacement General equation : x=A Sin(Kt) where

A= amplitude , t=time and K=frequency. Hence the unit of K is Hertz.

Answer 2

Answer: Hertz

Explanation: As the displacement of a particle is given by$x = A sin^2 (Kt)$, where t denotes the time.

As the displacement of particle  x$=A^2 sin^2(kt)$

$x=A^2sin^2$∅

∅=kt (Where ∅ is an angle→Dimensionless)

kt → dimensionless,

[k] = $\frac{1}{[t]}=T^-^1$

As we know, the formula of frequency → [$M^0L^0T^-^1$]

As frequency = Hertz.

Hence, the unit of K hertz.

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