A wheel of radius R rolls on the ground with a uniform velocity v . The relative acceleration of the topmost point of the wheel with respect to the bottommost point is

Question

A wheel of radius R rolls on the ground with a uniform velocity v . The relative acceleration of the topmost point of the wheel with respect to the bottommost point is (A) ( textitv2/ textitR) (B) ( text2 textitv2/ textitR) (C) ( textitv2/ text2 textitR) (D) ( text4 textitv2/ textitR)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-p5tlxft8lyv0.png" /> As it is rolling ⇒ ω =(V/R) VQ=0 ⇒ VP / Q=ω (. 2 R .)=2V ⇒ aP / Q=(VP / Q 2/2 R)=((. 2 V .)2/2 R)=(2 V2/R)

Q. A wheel of radius $R$ rolls on the ground with a uniform velocity $v$ . The relative acceleration of the topmost point of the wheel with respect to the bottommost point is

$\frac{v ^{2}}{R}$

$\frac{2 v ^{2}}{R}$

$\frac{v ^{2}}{2 R}$

$\frac{4 v ^{2}}{R}$

As it is rolling
$\Rightarrow ω = \frac{V}{R}$
$V_{Q} = 0$
$\Rightarrow V_{P / Q} = ω (2 R) = 2 V$
$\Rightarrow a_{P / Q} = \frac{V _{P / Q}^{2}}{2 R} = \frac{( 2 V ) ^{2}}{2 R} = \frac{2 V ^{2}}{R}$

Q. A wheel of radius R rolls on the ground with a uniform velocity v . The relative acceleration of the topmost point of the wheel with respect to the bottommost point is

Rv2​

R2v2​

2Rv2​

R4v2​