Question

A boy whirls a stone in a horizontal circle of radius 1.4 m and at height 1.5 m above ground level. The string breaks, and the stone flies horizontally and strikes the ground after traveling a horizontal distance of 10 m. What is the magnitude of the centripetal acceleration of the stone while in circular motion?

Answer 1

Answer:$233.23 m/s^2$

Explanation:

Given

radius of circle=1.4 m

Height of stone above ground=1.5 m

Horizontal distance(R)=10 m

It is given at the time of break stone flies horizontally thus stone to cover a height of 1.5 m in time t before reaching ground

$1.5=0+\frac{gt^2}{2}$

t=0.55 s

Initial horizontal velocity at the time of break is given by u

$R=u\times t$

$10=u\times 0.55$

u=18.07 m/s

Therefore magnitude of centripetal acceleration is given by

$a_c=\frac{u^2}{r}=\frac{18.07^2}{1.4}=233.23 m/s^2$