A wheel of radius 1 m rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is :

Question

A wheel of radius 1 m rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is : (A)  2π  (B)  √2π  (C)  √π 2+4  (D)  π

Tardigrade Admin · Accepted Answer

When wheel rolls half a revolution, the point (P) of the wheel which is in contact with the ground initially, moves at the top of the wheel as shown.

Horizontal displacement of wheel,

x = π r,

where r being the radius.
Vertical displacement of point P,

y = 2 r

Net displacement

= x^{2} + y^{2}

= (π r)^{2} + (2 r)^{2}

= r π^{2} + 4

= π^{2} + 4

(∵ r = 1 m)

Q. A wheel of radius $1 m$ rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is :

$2 π$

$2 π$

$π^{2} + 4$

$π$

Q. A wheel of radius 1m rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is :

2π

2π​

π2+4​

π

Q. A wheel of radius $1 m$ rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is :

$2 π$

$2 π$

$π^{2} + 4$

$π$