A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30°. The centre of mass of cylinder has speed of 4 m/s. The distance travelled by the cylinder on the incline surface will be (Take g = 10 ) [2019]

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Solution

Q.
A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30°. The centre of mass of cylinder has speed of 4 m/s. The distance travelled by the cylinder on the incline surface will be (Take g = 10 $m / s^{2}$ ) [2019]

1 2.2 m

2 1.6 m

3 1.2 m

4 2.4 m

Ans.
(4)

Using law of conservation of energy,

$m g h = \frac{1}{2} m v_{CM}^{2} + \frac{1}{4} m r^{2} ω^{2}$

$\Rightarrow m g s \sin 30 ° = \frac{1}{2} m v_{CM}^{2} + \frac{1}{4} m v_{CM}^{2}$

$\Rightarrow s = \frac{3}{4}$ $\frac{v_{CM}^{2}}{g \sin 30 °}$ $\Rightarrow s = \frac{3}{4} \times \frac{4^{2}}{10 \times \frac{1}{2}}$

$\Rightarrow s = \frac{3 \times 4 \times 2}{10} = \frac{12}{5} = 2.4 m$

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