An object at rest is suddenly broken apart into two fragments by an explosion. One fragment acquires twice the kinetic energy of the other. What is the ratio of their masses?

You are right. It is 1:2. Here is the procedure:

The kinetic energy of an object is given by the formula $KE = \frac{1}{2}mv^2$, where $m$ is the object's mass and $v$ is its velocity. Since one of the fragments has twice the kinetic energy of the other, we can write the following equation:

$\frac{1}{2}m_1v_1^2 = 2 \times \frac{1}{2}m_2v_2^2$

We can then solve for the ratio of the masses $m_1$ and $m_2$:

$m_1 = \frac{m_2}{2} \Rightarrow \frac{m_1}{m_2} = \frac{1}{2}$

Therefore, the ratio of the masses of the two fragments is 1 to 2.