Respuesta :
Answer:
f= 0.48 s⁻¹
Explanation:
Given that
Mass of the ladder ,m= 6 kg
L= 2 m
Mass of artist ,M= 42 kg
The total moment of inertia of the both ladder and artist ,I
[tex]I=\dfrac{mL^2}{3}+ Mr^2[/tex]
Here[tex] r=\dfrac{L}{2}[/tex]
[tex]I=\dfrac{mL^2}{3}+ M\dfrac{L^2}{4}[/tex]
[tex]I=\dfrac{6\times 2^2}{3}+ 42\times \dfrac{2^2}{4}\ kg.m^2[/tex]
I=50 kg.m²
The angular frequency f given as
[tex]f=\dfrac{1}{2\pi}\times\sqrt{ \dfrac{m_t\ g D}{I}}[/tex]
Here [tex]m_t= m +M[/tex]
[tex]D=\dfrac{L}{2}\ m[/tex]
[tex]D=\dfrac{2}{2}\ m[/tex]
D=1 m
[tex]f=\dfrac{1}{2\pi}\times\sqrt{ \dfrac{(42+6)\times 9.81\times 1}{50}}\ s^{-1}[/tex]
f= 0.48 s⁻¹
