Question

A body is moving on a circle of radius 80 m with a speed $20m/s^2$ which is decreasing at the rate $5m/s^2$ at an instant. The angle made by its acceleration with its velocity is

• A. ${45}^o$
• B. ${90}^o$
• C. ${190}^o$
• D. ${135}^o$

Answer 1

The correct option is D ${135}^o$

Centrapetal acceleration ,$a_c=\frac{v^2}{r}=\frac{{20}^2}{80}$

=$5m/s^2$

If the brake is applied in the movement of body at P of circular turn , acceleration along the target $=5m/sec$

Angle between both the acceleration $={90}^{\circ }$

the magnitude of resultant acceleration

$a=\sqrt{a_c^2+a_5^2}=\sqrt{5^2+5^2}=5\sqrt{2}m/se{c}^{@}$

List the resultant acceleration make an angle $\theta$ with tangent

$tan\theta =\frac{a_c}{a_5}=\frac{5}{5}=1$

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

Therefore required angle is ${90}^{\circ }+{45}^{\circ }$

$={135}^{\circ }$