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**1. Homework Statement**

As show in the figure below, balloon A (containing gas of density ##ρ_A##) and balloon B (containing gas of density ##ρ_B##) are each suspended by string from the ceiling of a train at rest. Balloon C (containing gas of density ##ρ_C## is attached to the train floor by string, and floats above the floor. The density of the air is ##ρ_o##, where ##ρ_C<ρ_o<ρ_B<ρ_A##. The balloon's mass, the string's mass at the movement of air inside the train are negligible.

The train begins moving with uniform accleration in a horzizontal direction (to the right in the figure). A, B, S come to rest with respect to the train and form, respectively, angles ##\theta_A;\theta_B;\theta_C## with the vertical. Choose the best represents the condition inside the train at this time.

**2. Homework Equations**

F=-ma

**3. The Attempt at a Solution**

$$tan \theta_A=\frac{g\rho_A V-g\rho_oV}{V\rho_Aa}$$

$$tan \theta_B=\frac{g\rho_B V-g\rho_oV}{V\rho_Ba}$$

Because ##\dfrac{\rho_A-\rho_o}{\rho _A}>\dfrac{\rho_B-\rho_o}{\rho _B}##

and I choose 1. But the answer is 4. Where is my wrong?

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