Part BCSIR NET June 2025p-dot-is-the-partial-of-L-in-q-so-a-plus-q-squared-term-pushes-outward

P dot is the partial of L in q so a plus q squared term pushes outward

Suppose a dynamical system has the Lagrangian L = (q̇ $_{1})^{2} + (q$ ̇ $_{2})^{2} + (q_{1})^{2} + q$ ̇ $_{1} q$ ̇ $_{2}$ . If $p_{1}$ and $p_{2}$ are momenta conjugate to $q_{1}$ and $q_{2}$ respectively, then which of the following statements is true?

A.ṗ $_{1} = 2 q_{1}$ , ṗ $_{2} = 0$ ✓
B.ṗ $_{1} = - q_{1}$ , ṗ $_{2} = 0$
C.ṗ $_{1} = - q_{1} /2, p_{2} = q_{2}$
D.ṗ $_{1} = q_{1}, p_{2} = - q_{2}$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

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P dot is the partial of L in q so a plus q squared term pushes outward

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