SATHEE: Rotational Motion Question 48

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) $\sqrt{π^{2} + 4} m$

C) $π m$

D) $\sqrt{π^{2} + 2} m$

Show Answer

Answer:

Correct Answer: B

Solution:

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

Vertical displacement, $y = 2 R$

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

$s = \sqrt{x^{2} + y^{2}}$

$= \sqrt{{(π R)}^{2} + {(2 R)}^{2}}$

$= \sqrt{π^{2} R^{2} + 4 R^{2}}$

But $R = 1 m$ (given)

$∴$ $s = \sqrt{π^{2} {(1)}^{2} + 4 {(1)}^{2}}$ $= \sqrt{π^{2} + 4} m$

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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:

Options:

Answer:

Solution:

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