Physics GRE - #14

The figure below shows a small mass connected to a string, which is attached to a vertical post.

If the mass is released when the string is horizontal as shown, the magnitude of the total acceleration of the mass as a function of the angle $\theta$ is:

• $g\sin\theta$
• $2g\cos\theta$
• $2g\sin\theta$
• $g\sqrt{3\cos^2{\theta}+1}$
• $g\sqrt{3\sin^2{\theta}+1}$

Solution :

We know that at $\theta=0$, the acceleration of the mass is exactly $g$. The only solution that satisfies this boundary condition is the last choice.