A force F ⃗ \vec{F} F =α i ^ + 3 j ^ + 6 k ^ \hat{i}+3\hat{j}+6\hat{k} i ^ + 3 j ^ + 6 k ^ acts at r=2 i ^ − 6 j ^ − 12 k ^ \hat{i}-6\hat{j}-12\hat{k} i ^ − 6 j ^ − 12 k ^ . Find α for conservation of angular momentum about the origin.
Physics · Rotational Motion · torque and rotational equilibrium
AIPMT July 2015 NEET

Question

A force F ⃗ \vec{F} F =α i ^ + 3 j ^ + 6 k ^ \hat{i}+3\hat{j}+6\hat{k} i ^ + 3 j ^ + 6 k ^ acts at r=2 i ^ − 6 j ^ − 12 k ^ \hat{i}-6\hat{j}-12\hat{k} i ^ − 6 j ^ − 12 k ^ . Find α for conservation of angular momentum about the origin.

Physics · Rotational Motion · torque and rotational equilibrium

AIPMT July 2015 NEET

G1 Physics · Accepted Answer

Step 1: Angular momentum is conserved when external torque r×F=0. Step 2: Thus F must be parallel to r. Step 3: Ratios 3/(-6)=6/(-12)=-1/2 imply α/2=-1/2, hence α=-1. Final answer: A — -1.

A force F ⃗ \vec{F} F =α i ^ + 3 j ^ + 6 k ^ \hat{i}+3\hat{j}+6\hat{k} i ^ + 3 j ^ ​ + 6 k ^ acts at r=2 i ^ − 6 j ^ − 12 k ^ \hat{i}-6\hat{j}-12\hat{k} i ^ − 6 j ^ ​ − 12 k ^ . Find α for conservation of angular momentum about the origin.

A force F ⃗ \vec{F} F =α i ^ + 3 j ^ + 6 k ^ \hat{i}+3\hat{j}+6\hat{k} i ^ + 3 j ^ + 6 k ^ acts at r=2 i ^ − 6 j ^ − 12 k ^ \hat{i}-6\hat{j}-12\hat{k} i ^ − 6 j ^ − 12 k ^ . Find α for conservation of angular momentum about the origin.