Question

5) A motor cyclist is performing vertical circular motion inside sphere. His speed
Is 6m/s calculate diameter of sphere.​

Answer 1

Given:

A motor cyclist is performing vertical circular motion inside a sphere. His speed at the bottom of the sphere is 6 m/s

To find:

Diameter of sphere

Calculation:

For successful completion of a vertical circle, the minimum velocity to be present at the bottom of the sphere is √(5gL) and at the top is √(gL) .

Here , g refers to gravity and L refers to the radius of the the vertical circle.

$\therefore \: \sqrt{5gL} = 6$

$= > \: 5gL = {6}^{2} = 36$

$= > L = \dfrac{36}{5g}$

$= > L = \dfrac{36}{5 \times 10}$

$= > \: L = 0.72 \: m$

Diameter will be 2L = 1.44 m

So, final answer is:

Diameter of the sphere is 1.44 m.