Question

A point P on the rim of wheel is initially at rest and in
contact with the ground. Find the displacement of the point
P if the radius of the wheel is 5 m and the wheel rolls
forward through half a revolution
[Kerala (Engg.) 2001; CBSE PMT 2002)​

Answer 1

the displacement of the point  P if the wheel rolls  forward through half a revolution is 5√(π²+4)

Explanation:

Given the radius of the wheel R = 5m

As shown in the figure, the point P will reach at P'after half a revolution

The distance covered on the ground by the wheel due to rolling after half a revolution will be πR

The displacement of the point P will be PP'

In right angled triangle PQP'

$PP'^2=PQ^2+QP'^2$

$\implies PP'^2=(\pi R)^2+(2R)^2$

$\implies PP'^2=R^2(\pi^2+4)$

$\implies PP'=R\sqrt{\pi^2+4}$

Putting the value of R = 5m, we get the displacement of point P

$=5\sqrt{\pi^2+4}$

Hope this answer is helpful.

Know More:

Q: What is the displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward a revolution? take the radius of the wheel as R and the x-axis as the forward direction? along with steps.

Click Here: https://brainly.in/question/1295962

Q. A wheel of radius 1 metre rolls forward half a Revolution on a horizontal ground find the magnitude of the displacement of the point of the wheel initially in contact with the ground.

Click Here: https://brainly.in/question/4419804