A homogeneous shaft $\text{PQR}$ with fixed supports at both ends is subjected to a torsional moment $\mathrm{T}$ at point $\mathrm{Q}$, as shown in the figure. The polar moments of inertia of the portions $\text{PQ}$ and $\text{QR}$ of the shaft with circular cross-sections are $\text{J}_{1}$ and $\text{J}_{2}$, respectively. The torsional moment reactions at the supports $\mathrm{P}$ and $\mathrm{R}$ are $\mathrm{T}_{\mathrm{P}}$ and $\mathrm{T}_{\mathrm{R}}$, respectively.
If $\mathrm{T}_{\mathrm{P}} / \mathrm{T}_{\mathrm{R}}=4$ and $\mathrm{J}_{1} / \mathrm{J}_{2}=2$, the ratio of the lengths $\mathrm{L}_{1} / \mathrm{L}_{2}$ is
- $0.50$
- $0.25$
- $4.00$
- $2.00$