10. If $0<x \leqslant 1, a=\left(\frac{\sin x}{x}\right)^{2}, b=\frac{\sin x}{x}$, $c=\frac{\sin x^{2}}{x^{2}}$. Then the size relationship of $a, b, c$ is $\qquad$ .
10. $a<b \leqslant c$.

When $0<x \leqslant 1 \leqslant \frac{\pi}{2}$, $\sin x<x$. Therefore, $0<\frac{\sin x}{x}<1$.
Thus, $\left(\frac{\sin x}{x}\right)^{2}<\frac{\sin x}{x}$, which means $a<b$.
Since $y=\frac{\sin x}{x}$ is a decreasing function on $(0,1]$, we have $\frac{\sin x}{x}<\frac{\sin x^{2}}{x^{2}}$, which means $b<c$.
However, when $x=1$, $b=c$. Hence, $a<b \leqslant c$.