Question

In $U.C.M.$, when time interval $\delta t\to 0$, the angle between change in velocity $(\delta v)$ and linear velocity $(v)$ will be

• A. $0^{\circ }$
• B. $90^{\circ }$
• C. $180^{\circ }$
• D. $45^{\circ }$

Answer 1

Answer: (B)

The direction of change in velocity ($\delta v$) is given by
$\varphi =\frac{180^{\circ }-\theta }{2}=90^{\circ }-\frac{\theta }{2}...(i)$
This can be shown graphically as

For small time interval, i.e., $\delta t\to 0$, then angle between $v_1$ and $v_2$ is very small i.e., $\theta \approx 0^{\circ }$. So, from Eq. (i), we get
$\varphi =90^{\circ }$