A disc of radius R and mass M is rolling horizontally without slipping with speed n. It then moves up an inclined smooth surface as shown in the figure. The maximum height that the disc can go up the incline is _____

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Q.
A disc of radius R and mass M is rolling horizontally without slipping with speed n. It then moves up an inclined smooth surface as shown in the figure. The maximum height that the disc can go up the incline is ______ [2024]

1 $\frac{v^{2}}{g}$

2 $\frac{3}{4} \frac{v^{2}}{g}$

3 $\frac{1}{2} \frac{v^{2}}{g}$

4 $\frac{2}{3} \frac{v^{2}}{g}$

Ans.
(3)

Rolling $v_{0} = ω R$

Conservation of energy, $K_{i} + U_{i} = K_{f} + U_{f}$

$\frac{1}{2} m v_{0}^{2} + \frac{1}{2} [\frac{M R^{2}}{2}] {\cdot (\frac{v_{0}}{R})}^{2} + 0 = m g h + \frac{1}{2} [\frac{M R^{2}}{2}] \cdot (\frac{v_{0}^{2}}{R^{2}})$

$\frac{1}{2} m v_{0}^{2} = m g h_{\max} \Rightarrow h_{\max} = \frac{v_{0}^{2}}{2 g}$

Solution

Q.
A disc of radius R and mass M is rolling horizontally without slipping with speed n. It then moves up an inclined smooth surface as shown in the figure. The maximum height that the disc can go up the incline is ______ [2024]

1 $\frac{v^{2}}{g}$

2 $\frac{3}{4} \frac{v^{2}}{g}$

3 $\frac{1}{2} \frac{v^{2}}{g}$

4 $\frac{2}{3} \frac{v^{2}}{g}$

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Solution

Q. A disc of radius R and mass M is rolling horizontally without slipping with speed n. It then moves up an inclined smooth surface as shown in the figure. The maximum height that the disc can go up the incline is ______ [2024]

1 v2g

2 34v2g

3 12v2g

4 23v2g

Ans. (3) Rolling v0=ωR Conservation of energy, Ki+Ui=Kf+Uf 12mv02+12[MR22]·(v0R)2+0=mgh+12[MR22]·(v02R2) 12mv02=mghmax⇒hmax=v022g

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Q.
A disc of radius R and mass M is rolling horizontally without slipping with speed n. It then moves up an inclined smooth surface as shown in the figure. The maximum height that the disc can go up the incline is ______ [2024]

1 $\frac{v^{2}}{g}$

2 $\frac{3}{4} \frac{v^{2}}{g}$

3 $\frac{1}{2} \frac{v^{2}}{g}$

4 $\frac{2}{3} \frac{v^{2}}{g}$