Question

A particle moves in a circle of radius 4 cm clockwise at constant speed of 2 cm s^-1. If $\widehat{x}$and $\widehat{y}$are unit acceleration vectors along x and y axes, respectively, the acceleration of the particle at the instant half way between PQ is given by

• A. $- 4\left( \widehat{x} - \widehat{y} \right)$
• B. $4\left( \widehat{x} + \widehat{y} \right)$
• C. $\frac{- \left( \widehat{x} + \widehat{y} \right)}{\sqrt{2}}$
• D. $\frac{\widehat{x} - \widehat{y}}{4}$

Answer 1

Answer: (C)

$\frac{- \left( \widehat{x} + \widehat{y} \right)}{\sqrt{2}}$

Answer 2

Mid point acceleration,

a = $\frac{v^{2}}{r} = \frac{4}{4} = 1ms^{- 1}$ at 45⁰ with x axis

∴ ${\overrightarrow{a}}_{x} = - a\cos 45^{o}\widehat{x}$

= -1 × $\frac{1}{2}\widehat{x} = - \frac{1}{\sqrt{2}}\widehat{x}$

Thus $\widehat{a} = {\overrightarrow{a}}_{x} + {\overrightarrow{a}}_{y} = - \frac{1}{\sqrt{2}}\left( \widehat{x} + \widehat{y} \right)$