Question

A particle is rotating about a vertical axis in the horizontal plane such that the angular velocity of the particle about the axis is constant and is equal to $1 \,rad/s$. Distance of the particle from axis is given by $R=R_{0}-\beta t$ where $t$ stands for time. The speed of the particle as a function of time is

• A. $\sqrt{\beta ^{2} + 1}$
• B. $\left(R_{0} - \beta t\right)$
• C. $\sqrt{\beta ^{2} + R_{0} - \beta t^{2}}$
• D. $\beta $

Answer 1

Answer: (C)

$V_{\text{radial}}=\frac{d R}{d t}=-\beta $
$V_{\text{tangential}}=\omega R=\omega R_{0} - \beta t$
$V=\sqrt{V_{r}^{2} + V_{t}^{2}}=\sqrt{\beta ^{2} + R_{0} - \beta t^{2}}$