Respuesta :

skyluke89

Answer:

[tex]\frac{inertia_B}{inertia_A}=9[/tex]

Explanation:

First of all, let's remind that:

- The kinetic energy of an object is given by [tex]K=\frac{1}{2}mv^2[/tex], where m is the mass and v is the speed

- The momentum of an object is given by [tex]p=mv[/tex]

- The inertia of an object is proportional to its mass, so we can write [tex]I=km[/tex], where k just indicates a constant of proportionality

In this problem, we have:

- [tex]K_A = K_B[/tex] (the two objects have same kinetic energy)

- [tex]p_A = 3 p_B[/tex] (A has three times the momentum of B)

Re-writing both equation we have:

[tex]\frac{1}{2}m_A v_A^2 = \frac{1}{2}m_B v_B^2\\m_A v_A = 3 m_B v_B[/tex]

If we divide first equation by second one we get

[tex]v_A = 3 v_B[/tex]

And if we substitute it into the first equation we get

[tex]m_A (3 v_B)^2 = m_B v_B^2\\9 m_A v_B^2 = m_B v_B^2\\m_B = 9 m_A[/tex]

So, B has 9 times more mass than A, and so B has 9 times more inertia than A, and their ratio is:

[tex]\frac{I_B}{I_A}=\frac{km_B}{km_A}=\frac{9m_A}{m_A}=9[/tex]

onyebuchinnaji

The ratio of the inertia of objects A and object B is 3:1.

What is inertia?

Inertia is the measure of the reluctance of an object to move. Inertia depends on the mass of the object.

What is kinetic energy?

The kinetic energy of an object is the energy possessed by the object due to its motion.

K.E = ¹/₂mv²

[tex]v =\sqrt{ \frac{2K.E}{m} }[/tex]

[tex]v_a = \sqrt{\frac{2K.E}{m_a} } \\\\v_b = \sqrt{\frac{2K.E}{m_b} }[/tex]

What is momentum?

The momentum of an object is determined from the product of mass and velocity of an object.

P = mv

P(b) = mv

P(a) = 3P(b) = 3mv

Ratio of their inertias;

[tex]\frac{A}{B} = \frac{3M_bV_b}{M_bV_b} = 3:1[/tex]

Thus, the ratio of the inertia of objects A and object B is 3:1.

Learn more about inertia here: https://brainly.com/question/1140505

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