Question

A man in a minivan rounds a circular turn at a constant speed. Which of the following would cause the minivan to experience less acceleration:
A) Travelling faster.
B) Travelling around a turn with a smaller circular radius.
C) Travelling with more weight in the van.
D) Travelling around the turn with a greater circular radius.
E) Travelling the opposite direction around the same turn.

Answer 1

Hint: The acceleration experienced by the minivan is centripetal acceleration which has its direction always acting towards the centre of the circular track. The centripetal acceleration of the body under-going in circular motion depends upon the radius of the circular track as well as the linear velocity of the body.

Formula used:
The formula of the centripetal force on the body is given by,
${F_c} = \dfrac{{m{v^2}}}{R}$
Where ${F_c}$ is the centripetal force m is the mass of the body v is the velocity of the body and the R is the radius of the circular track.
The formula of the centripetal acceleration is given by,
${a_c} = \dfrac{{{v^2}}}{R}$
Where ${a_c}$ is the centripetal acceleration v is the velocity of the body and the R is the radius of the circular track.

Complete step by step answer:
It is given in the problem that a man in a minivan rounds a circular turn at a constant speed the minivan experiences an acceleration and we need to find a way to lessen this acceleration.
The acceleration that the minivan experiences are centripetal acceleration. Since the formula of the acceleration is given by,
${a_c} = \dfrac{{{v^2}}}{R}$
Where ${a_c}$ is the centripetal acceleration v is the velocity of the body and the R is the radius of the circular track.
Here the centripetal acceleration is inversely proportional to the radius of the circular track so if we want to decrease the centripetal acceleration we need to increase the radius of the circular track.
The decrease of the radius of the circular track will lessen the centripetal acceleration on the minivan.

Therefore, the correct option is option D.

Note:
The centripetal force that is experienced by the body under-going in a circular motion is inversely proportional to the radius of the circular turn and is proportional to the linear velocity of the body which is undergoing in the circular motion.