જ્યારે સ્થાન સદિશ \(\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}\) એ- \(\vec{r}\) અનુસાર ચિન્હ્ બદલે તો નીચેનામાંનો કયો સદિશ ચિન્હ્ બદલાવાથી ઉલટાશે નહીં?

A રેખીય વેગમાન
B વેગ
C પ્રવેગ
D કોણીય વેગમાન

Verified Solution

Answer & Solution

Correct Answer

(D) કોણીય વેગમાન

Step-by-step Solution

Detailed explanation

\(\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}\) \(\vec{v}=\frac{d\vec{r}}{dt}=v_{x}\hat{i}+v_{y}\hat{j}+v_{z}\hat{k}\) \(\vec{p}=m\vec{v}\) \(\overline{L}=m(\vec{r}\times\vec{v})\) \(=(x\hat{i}+y\hat{j}+z\hat{k})\times m(v_{x}\hat{i}+v_{y}\hat{j}+v_{z}\hat{k})\) જ્યારે \(\vec{r}\) ની…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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