logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class11  >>  Units and Measurement
0 votes

Suppose we are told that the acceleration $A$ of a particle moving with uniform speed $v$ in a circle of radius $r$ is proportional to some power of r, say $r^n$, and some power of v, say $v^m$. Which of the following is the simplest form of an equation for the acceleration?

$\begin {array} {1 1} (A) A = k \large\frac{v}{r} \\ (B) A = k \large\frac{v}{r^2} \\ (C) A = k \large\frac{v^2}{r} \\ (D) A = kvr \end {array}$

Can you answer this question?
 
 

1 Answer

0 votes
Given that Acceleration of the particle $A \propto r^n v^m$ where $v$ is the velocity and $r$ is the radius of the circle.
$A = k r^n v^m$, where $k$ is a dimensionless unit of propotionality.
We know that the formula for Acceleration $A = \large\frac{L}{T^2}$
$\Rightarrow$ Knowning the dimensions of $A$, $r$ and $v, \large\frac{L}{T^2} $$ = L^n \large(\frac{L}{T})^{\normalsize m}$
For this to be balanced, $n + m = 1 $ and $m = 2$ which means that $n = -1$.
Therefore, we can write the expression for acceleration as $A = k \large\frac{v^2}{r}$
answered Mar 23, 2014 by balaji.thirumalai
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...