The velocity and acceleration of a point-like body at the initial moment of its motion are v0 =8 m s- 1 and a=2 m s- 2 respectively. The acceleration vector of the body remains constant. The minimum radius of curvature of the trajectory of the body is

Question

The velocity and acceleration of a point-like body at the initial moment of its motion are v0 =8 m s- 1 and a=2 m s- 2 respectively. The acceleration vector of the body remains constant. The minimum radius of curvature of the trajectory of the body is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-wm6gdvaoqq6m.png" /> (A) 2m (B) 4m (C) 8m (D) 16m

Tardigrade Admin · Accepted Answer

The acceleration vector shall change the component of velocity u_II along the acceleration vector.

r = \frac{v ^{2}}{a _{n}}

The radius of curvature

r_{min}

means v is minimum and a_n is maximum. This is at the point

P

when the component of velocity parallel to the acceleration vector becomes zero, that is u_II = 0.
Solution

∴ R = \frac{u _{⊥}^{2}}{a} = \frac{4 ^{2}}{2} = 8 m

Q. The velocity and acceleration of a point-like body at the initial moment of its motion are $v_{0} = 8 m s^{- 1}$ and $a = 2 m s^{- 2}$ respectively. The acceleration vector of the body remains constant. The minimum radius of curvature of the trajectory of the body is

$2 m$

$4 m$

$8 m$

$16 m$

Q. The velocity and acceleration of a point-like body at the initial moment of its motion are v0​=8ms−1 and a=2ms−2 respectively. The acceleration vector of the body remains constant. The minimum radius of curvature of the trajectory of the body is

2m

4m

8m

16m

Q. The velocity and acceleration of a point-like body at the initial moment of its motion are $v_{0} = 8 m s^{- 1}$ and $a = 2 m s^{- 2}$ respectively. The acceleration vector of the body remains constant. The minimum radius of curvature of the trajectory of the body is

$2 m$

$4 m$

$8 m$

$16 m$