Question

A particle is moving with constant speed over circle $x^2 + y^2 = 50$, with speed $\sqrt{10} m/s$. Acceleration of the particle, when it is at point $(5, 5)$ is (in $m/s^2$)

• A. $\hat{i}-\hat{j}$
• B. $-\hat{i}-\hat{j}$
• C. $\frac{1}{\sqrt{2}}\hat{i} -\frac{1}{\sqrt{2}}\hat{j}$
• D. $\frac{-1}{\sqrt{2}}\hat{i} -\frac{1}{\sqrt{2}}\hat{j}$

Answer 1

Answer: (B)

$x^2 + y^2 = r^2$
$\Rightarrow r = \sqrt{50}$
$= 5\sqrt{2}$
$\vec{a_c} = \frac{u^2}{r}$
$ = \frac{(\sqrt{10})^2}{5\sqrt{2}} = \sqrt{2}$
Resolve it into components to get
$\vec{a_c} = -\hat{i} -\hat{j}$