Question

In the given figure, $a=15$ m/$s^2$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R=2.5$m at a given instant of time. The speed of the particle is:

• A. $6.2m/s$
• B. $4.5m/s$
• C. $5.0m/s$
• D. $5.7m/s$

Answer 1

The correct option is D $5.7m/s$

$\text{Step 1: Centripetal acceleration}$$\text{[Ref. Fig.]}$

Total acceleration has two components, i.e. tangential acceleration $\left(a_t\right)$ and centripetal acceleration $\left(a_c\right)$

From the figure $a_c=a\cos {30}^{\circ }$ $....\left(1\right)$

$\text{Step 2: Speed calculation}$

Centripetal acceleration is given by

$a_c=\frac{v^2}{R}$ $....\left(2\right)$

where $v$ is the speed of the particle.

From equation $\left(1\right)$ and $\left(2\right)$

$a\cos {30}^o=\frac{v^2}{R}$

$\Rightarrow$ $15\cos {30}^o=\frac{v^2}{2.5}$

$\Rightarrow v=\sqrt{32.5}m/s$$=5.7m/s$

Hence speed of the particle is $5.7m/s$. Option D is correct