Question

A particle moves in a circle of radius 4 cm clockwise at constant speed of 2 cm/s. If $\hat{x}$ and $\hat{y}$ are unit acceleration vectors along x and y directions respetively in $cm/{sec}^2$, 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. $\frac{-(\hat{x}+\hat{y})}{\sqrt{2}}$
• D. $\frac{(\hat{x}+\hat{y})}{4}$

Answer 1

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

$a=\frac{v^2}{r}=\frac{4}{4}=1m/s^2{45}^o$ with x-axis

$\overrightarrow{a_x}=-a\text{cos}{45}^o\hat{x}$

$=-1\ast \frac{1}{\sqrt{2}\hat{x}}$

$\overrightarrow{a_y}=-a\text{cos}{45}^o\hat{y}$

$=-1\ast \frac{1}{\sqrt{2}\hat{y}}$

$\overrightarrow{a}=\overrightarrow{a_x}+\overrightarrow{a_y}$

$=\frac{-1}{2}(\hat{x}+\hat{y})$