Question

A person on a yellow bicycle rounds a circular turn of radius, r with a speed v. Another person on a green bicycle rounds a different circular turn with a radius 3r at a speed 3v. Which bicycle experiences a greater acceleration , and how many times greater?

• A. yellow-9 times greater
• B. green-9 times greater
• C. yellow-3 times greater
• D. green -3 times greater
• E. same acceleration for each bicycle

Answer 1

Answer: (D)

green -3 times greater

Centripetal acceleration is given by $a=\frac{u^2}{R}$

where $u$ and $R$ are the velocity of the object and radius of cirlular path respectively.

Centripetal acceleration experienced by yellow bicycle $a_y=\frac{v^2}{r}$

Centripetal acceleration experienced by green bicycle $a_g=\frac{(3v{)}^2}{\left(3r\right)}=3\frac{v^2}{r}=3a_y$

Thus green bicycle experiences greater acceleration i.e $a_g=3a_y$