Question

In the given figure , $a=10\sqrt{2}{\text{m/s}}^2$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R=2\text{m}$ at a given instant of time. Speed of the particle is

• A. $2\sqrt{5}\text{m/s}$
• B. $3\sqrt{5}\text{m/s}$
• C. $5\sqrt{2}\text{m/s}$
• D. $5\sqrt{3}\text{m/s}$

Answer 1

The correct option is A $2\sqrt{5}\text{m/s}$

Given, Acceleration, $a=10\sqrt{2}{\text{m/s}}^2$
Radius, $R=2\text{m}$
According to question,

we know that for circular motion.
$a_c=\frac{v^2}{R}$
$\Rightarrow \text{a cos}{45}^{\circ }=\frac{v^2}{R}\Rightarrow v=\sqrt{2\times 10\sqrt{2}\times \frac{1}{\sqrt{2}}}$
$\Rightarrow v=2\sqrt{5}\text{m/s}$