Rotational Motion Question 86

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

Options:

A) - 1

B) 2

C) zero

D) 1

Show Answer

Answer:

Correct Answer: A

Solution:

  • Key Concept When the resultant external torque acting on a system is zero, the total angular momentum of a system remains constant.

    This is the principle of the conservation of angular momentum.

    Given, force F=αi^+3j^+6k^ is acting at a point r=2i^6j^12k^

    As, angular momentum about origin is conserved.

    i.e.τ= constant

    Torque, τ=0r×F=0

    |i^j^k^2612α36|=0

    (36+36)i^(12+12α)j^+(6+6α)k^=0

    So value of a for angular momentum about origin is conserved, α=1 .



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