First slide

Circular motion

Question

The figure shows the velocity and acceleration of a point like body at the initial moment of its motion. The acceleration vector of the body remains constant. The minimum radius of curvature of trajectory of the body is

Moderate

A

2 m
B

3 m
C

8 m
D

16 m

Solution

The acceleration vector shall change the component of velocity $u_{∥}$ along the acceleration vector.
$r = \frac{v^{2}}{a_{n}}$
Radius of curvature r_min means v is minimum and a_n is maximum. This is at point P when component of velocity parallel to acceleration vector becomes zero, that is $u_{∥} = 0$
$∴ R = \frac{u_{⊥}^{2}}{a} = \frac{4^{2}}{2} = 8 m$

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