A force F→=αi^+3j^+6k^ is acting at a point r→=2i^-6j^-12k^ . The value of α for which angular momentum about origin is conserved is:

Correct answer: (D) −1. If L→= constant then τ→=0 So r→×F→=0⇒F→ should be parallel to r→ so coefficient should be in same ratio. So (α)/2=3/(-6)=6/(-12) So α=-1

Q103 / 180 · NEET 2015 (Phase 2) · Physics

A force $\vec{F} = α \hat{i} + 3 \hat{j} + 6 \hat{k}$ is acting at a point $\vec{r} = 2 \hat{i} - 6 \hat{j} - 12 \hat{k}$ . The value of $α$ for which angular momentum about origin is conserved is:

A
$2$
B
Zero
C
$1$
Correct answer
D
$- 1$

Solution

\vec{L} =

constant then

\vec{τ} = 0

\vec{r} \times \vec{F} = 0 \Rightarrow \vec{F}

should be parallel to

\vec{r}

so coefficient should be in same ratio. So

\frac{α}{2} = \frac{3}{- 6} = \frac{6}{- 12}

α = - 1

Hence, the correct answer is option: 'D'.

Relevant Questions

A thin horizontal disc is rotating about a vertical axis passing through its fixed centre . Its angular momentum is and computed about point2026 (Re-NEET)Angular momentum and Angular impulse
The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radi2025Angular momentum and Angular impulse
A solid sphere is rotating freely about its symmetric axis in free space. The radius of the sphere is increased keeping its mass same. Which2018Angular momentum and Angular impulse
Two discs of same moment of inertia ( I ) are rotating in same sense about their regular axis passing through centre and perpendicular to th2017Angular momentum and Angular impulse
Two rotating bodies, A and B of masses, m and 2 m with moments of inertia. I A and I B I B I A have equal kinetic energy of rotation. If, L 2016 (Phase 2)Angular momentum and Angular impulse
A mass m moves in a circle on a smooth horizontal plane with velocity v 0 at a radius R 0 . The mass is attached to a string which passes th2015 (Phase 1)Angular momentum and Angular impulse