Question

A body of mass m moves in a circular path with uniform angular velocity. The motion of the body has constant:

• A. Acceleration
• B. Velocity
• C. Momentum
• D. Kinetic energy

Answer 1

The correct option is D Kinetic energy

In circular motion

$\overrightarrow{v}=\overrightarrow{w}\times \overrightarrow{r}$

Since in circular motion a body changes its direction continually and hence changes its radial vector

Now,

If angular velocity $\overrightarrow{w}$ is constant then for the different radial vector $({\overrightarrow{r}}_1,{\overrightarrow{r}}_2,{\overrightarrow{r}}_3)$ there will be different velocity of body $(i.e.{\overrightarrow{v}}_1,{\overrightarrow{v}}_2,{\overrightarrow{v}}_3)$ as shown in figure

The centripetal acceleration of body will be to wards centre but for different position of body there will be different acceleration vector $({\overrightarrow{a}}_1,{\overrightarrow{a}}_2,{\overrightarrow{a}}_3)$ as shown in fig

momentum is given by

$\overrightarrow{P}=m\overrightarrow{v}$

Since velocity vector is changing

hence, $\overrightarrow{P}$ will change

In circular motion shown in figure

$|{\overrightarrow{r}}_1|=|{\overrightarrow{r}}_2|=|{\overrightarrow{r}}_3|=r$ (radius of circle)

$\Rightarrow |\overrightarrow{v}|=|\overrightarrow{w}|r$

Since $r$ and $|\overrightarrow{w}|$ is constant therefore $|\overrightarrow{v}|$ is constant for any position of body

We know that kinectic energy $\left(k\right)$

$k=\frac{1}{2}m|\overrightarrow{v}{|}^2$

$\Rightarrow$ kinectic energy $\left(k\right)$ of body will be constant