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shutvik [7]
2 years ago
8

If two objects A and B have the same kinetic energy but A has three times the momentum of B, what is the ratio of their inertias

?
Physics
1 answer:
Thepotemich [5.8K]2 years ago
7 0

Answer:

\frac{inertia_B}{inertia_A}=9

Explanation:

First of all, let's remind that:

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

- The momentum of an object is given by p=mv

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

In this problem, we have:

- K_A = K_B (the two objects have same kinetic energy)

- p_A = 3 p_B (A has three times the momentum of B)

Re-writing both equation we have:

\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

If we divide first equation by second one we get

v_A = 3 v_B

And if we substitute it into the first equation we get

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

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

\frac{I_B}{I_A}=\frac{km_B}{km_A}=\frac{9m_A}{m_A}=9

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