Question

A particle moves in a circle of radius $4cm$ clockwise at constant speed $2cm/s$. If $\hat{x}$ and $\hat{y}$ are unit acceleration vector along x and y-axis respectively (in $cm/s^2$), the acceleration of the particle at the instant half way between P and Q is given by

• A. $-4(\hat{x}+\hat{y})$
• B. $4(\hat{x}+\hat{y})$
• C. $-(\hat{x}+\hat{y})/\sqrt{2}$
• D. $(\hat{x}-\hat{y})/4$

Answer 1

The correct option is C $-(\hat{x}+\hat{y})/\sqrt{2}$

Radial acceleration $a_r={\omega }^{2}r=\frac{v^2}{r}=2^2/4=1c{m}^2/s$

Now this acceleration is directed toward origin in third quadrant.

Component of acceleration along negative x axis is $a_x=-a_{r}cos45\hat{x}$

Component of acceleration along negative y axis is $a_y=-a_{r}sin45\hat{y}$

${\overrightarrow{a}}_r=a_x+a_y=\frac{-(\hat{x}+\hat{y})}{\sqrt{2}}$