Rotational Motion Question 48

Question: P is the point of contact of a wheel and the ground. The radius of wheel is 1 m. The wheel rolls on the ground without slipping. The displacement of point P when wheel completes half rotation is:

[AIPMT 2002]

Options:

A) 2 m

B) π2+4m

C) πm

D) π2+2m

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Answer:

Correct Answer: B

Solution:

  • When the wheel rolls on the ground without slipping and completes half rotation, point P takes new. Horizontal displacement, x=πR

    Vertical displacement, y =2R

    Thus, displacement of the point P when wheel completes half rotation,

    s=x2+y2

    =(πR)2+(2R)2

    =π2R2+4R2

    But R=1m (given)

    s=π2(1)2+4(1)2 =π2+4m



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