Question

A point P is located on the rim of wheel of radius r = 0.5 m which rolls without slipping along a horizontal surface then the total distance traversed by the point P in meters between two successive moments it touches the surface is ______ m.

Options

• 4

• 5

• 6

• 7

Answer 1

A point P is located on the rim of wheel of radius r = 0.5 m which rolls without slipping along a horizontal surface then the total distance traversed by the point P in meters between two successive moments it touches the surface is 4 m.

Explanation:

V_p = `sqrt("V"^2+"V"^2+2"V"^2cos(pi-theta))`

V_p = 2V sin`(θ/2)`

Now V_p = `"ds"/"dt" = "ds"/"dv"."dv"/"dt"`

⇒ V_p = `omega"ds"/("d"theta) = "V"/"R" "ds"/("d"theta)`

⇒ `"V"/"R" "ds"/("d"theta) = 2"V"sin(theta/2)`

⇒ ds = 2R sin `(theta/2)`dθ

⇒ S = 2R `int_0^(2pi)sin(theta/2)`dθ

= 8 R 

= 4 m