NEET
- Exam
- NEET
- Subject
- Physics
- Chapter
- Rotational Motion
NEET · Physics · Rotational Motion
The torque T on a body about a given point is found to be equal to...
The torque T on a body about a given point is found to be equal to (\mathrm{A} \times \mathrm{L}) where A is constant vector, and is the angular momentum of the body about that point. From this it follows that
(A) (\frac{\mathrm{dL}}{\mathrm{dt}}) is perpendicular to L at all instants of time
(B) the component of L in the direction of A does not change with time.
(C) the magnitude of L does not change with time.
(D) L does not change with time
Options
- AA, B, C
- BA, C, D
- CB, C, D
- DA, B, C, D
Correct answer
A. A, B, C
Step-by-step solution
()
Given that
(\hat{}=\ddot{} )
()
From cross-product rule, () is always perpendicular to the plane containing and L
By the dot product definition
(\vec{L} . \vec{L}=L²)
Differentiating with respect to time
(\stackrel{}{} 2 )
(\Rightarrow \quad 2 L 2 L )
Since () is perpendicular to (L \Rightarrow 0 \Rightarrow L=) constant