NTA Abhyas 2020
- Exam
- NTA Abhyas
- Year
- 2020
- Subject
- Physics
- Chapter
- Motion in Two Dimensions
NTA Abhyas 2020 · Physics · Motion in Two Dimensions
The position vector of the particle is r(t) = acos ^ i + asin ^ j ,...
The position vector of the particle is r\left(t\right) = acos \omegat\overset{^}{i} + asin \omegat\overset{^}{j}, where and are real constants of suitable dimensions. The acceleration is
Options
- APerpendicular to the velocity
- BParallel to the velocity
- CDirected away from the origin
- DPerpendicular to the position vector
Correct answer
A. Perpendicular to the velocity
Step-by-step solution
Given that, r\left(t\right) = acos \omegat\overset{^}{i} + asin \omegat\overset{^}{j}
∵ \overset{→}{v} = \dfrac{dr\left(t\right)}{dt} = - a\omega sin \omegat\overset{^}{i} + a\omega cos \omegat\overset{^}{i}j
\overset{→}{a} = \dfrac{d\overset{→}{v}}{dt} = - a{\omega}^{2}cos \omegat\overset{^}{i} - a{\omega}^{2}cos \omegat\overset{^}{j}
Above result implies that acceleration is perpendicular to velocity.
∵ \overset{→}{v} = \dfrac{dr\left(t\right)}{dt} = - a\omega sin \omegat\overset{^}{i} + a\omega cos \omegat\overset{^}{i}j
\overset{→}{a} = \dfrac{d\overset{→}{v}}{dt} = - a{\omega}^{2}cos \omegat\overset{^}{i} - a{\omega}^{2}cos \omegat\overset{^}{j}
Above result implies that acceleration is perpendicular to velocity.