Question

A body is moving on a circle of radius $80m$ with a speed $20m/s$ which is decreasing at the rate $5m/s$ at an instant. The angle made by its acceleration with its velocity is

• A. $45$
• B. $90$
• C. $135$
• D. $0$

Answer 1

The correct option is A $45$

$a_t=5m/s^2$

$a_c=\frac{v^2}{r}=20\times 20\times \frac{1}{80}=4m/s^2$

angle made by

${\overrightarrow{a}}_{net}=\frac{a_t}{a_c}=\frac{5}{5}=1$

a tangential and velocity is in same direction

$tan\theta =1$

$\theta ={45}^{\circ }$

so (A) option is correct answer.