Question

A wheel starting from rest, rotates with $5{\text{rad/s}}^2$ angular acceleration along its axis. After $2\text{s}$ of motion, the magnitude of radial and tangential component of acceleration of the particle at a distance $2\text{cm}$ from the axis are ________ and ________ ${\text{cm s}}^{-2}$.

• A. $200,5$
• B. $50,10$
• C. $100,5$
• D. $200,10$

Answer 1

The correct option is D $200,10$

Given, $\alpha =5{\text{rad/s}}^2,t=2\text{s}$ and
$r=2\text{cm}$

Now to find the radial and tangential component of the acceleration

$a_t=r\alpha =5\times 2=10{\text{cm/s}}^2$
$(\because \omega ={\omega }_0+\alpha t=0+5\times 2=10\text{rad/s})$
$a_r=r{\omega }^2=2\times {10}^2=200{\text{cm/s}}^2$

Hence option D is the correct answer