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Units And Measurement

Question
CBSEENPH11020654

straight A space force space straight F space equals space straight alpha stack space straight i with hat on top space plus space 3 space straight j with hat on top space plus space 6 space straight k with hat on top space is space acting space at space straight a space point space straight r equals space 2 straight i with hat on top space minus space 6 space straight j with hat on top space minus 12 space straight k with hat on top. The value of α for which angular momentum about origin is conserved is
  • -1

  • 2

  • zero

  • 1

Solution

A.

-1

When the resultant external torque acting on a system is zero, the total angular momentum of a system is zero, the total angular momentum of a system remains constant.This is the principle of the conservation of angular momentum.
Given,
straight F space equals space straight alpha space straight i with hat on top space plus 3 space straight j with hat on top space plus space 6 space straight k with hat on top space is space acting space at space straight a space point space straight r equals space 2 space straight i with hat on top space minus 6 space straight j with hat on top space minus 12 space straight k with hat on top
As comma space angular space momentum space about space origin space is space consverved
straight i. straight e. comma
Torque space equals space constant
rightwards double arrow space Torque space equals space 0 space rightwards double arrow space straight r space xF space equals space 0

open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 2 cell negative 6 end cell cell negative 12 end cell row straight alpha 3 6 end table close vertical bar space equals space 0

rightwards double arrow space left parenthesis negative 36 space plus 36 right parenthesis straight i with hat on top space minus space left parenthesis 12 space plus space 12 straight alpha right parenthesis space straight j with hat on top space plus left parenthesis 6 space plus 6 straight alpha right parenthesis space straight k with hat on top space equals 0

rightwards double arrow space 0 space straight i with hat on top space minus space 12 space straight i with hat on top space left parenthesis space 1 plus straight alpha right parenthesis straight i with hat on top space plus space 6 space left parenthesis 1 space plus space straight alpha right parenthesis straight k with hat on top space equals 0

6 space left parenthesis 1 space plus straight alpha right parenthesis space equals 0 space rightwards double arrow space straight alpha space equals negative 1