A disc of radius R and mass M is rolling horizontally without slipping with speed v. It then moves up an incline as shown in figure. The maximum height upto which it can reach is

Question

A disc of radius R and mass M is rolling horizontally without slipping with speed v. It then moves up an incline as shown in figure. The maximum height upto which it can reach is (A) v2 / g (B) v2 / 2 g (C) v2 / 3 g (D) 3 v2 / 4 g

Tardigrade Admin · Accepted Answer

(1/2) M v2+(1/2) I ω2=M g h ⇒ (1/2) M v2+(1/2) (1/2) M R2((v/R))2=M g h ⇒ h=(3 v2/4 g)

Q. A disc of radius $R$ and mass $M$ is rolling horizontally without slipping with speed $v$ . It then moves up an incline as shown in figure. The maximum height upto which it can reach is

$v^{2} / g$

$v^{2} /2 g$

$v^{2} /3 g$

$3 v^{2} /4 g$

$\frac{1}{2} M v^{2} + \frac{1}{2} I ω^{2} = M g h$
$\Rightarrow \frac{1}{2} M v^{2} + \frac{1}{2} \frac{1}{2} M R^{2} (\frac{v}{R})^{2} = M g h \Rightarrow h = \frac{3 v ^{2}}{4 g}$

Q. A disc of radius R and mass M is rolling horizontally without slipping with speed v. It then moves up an incline as shown in figure. The maximum height upto which it can reach is

v2/g

v2/2g

v2/3g

3v2/4g