Question

Q. 21. A ring and a disc roll down an inclined plane
through the same height. Compare their speeds at
the bottom of the plane.
(1 mark)​

Answer 1

Answer:

ring will move faster than the disk roll

Answer 2

Given that,

A ring and a disc roll down an inclined plane  through the same height.

We need to calculate the speed of ring at the bottom

Using work energy theorem

$W=\Delta K.E$

$mgh=\dfrac{1}{2}I\omega^2$

$mgh=\dfrac{1}{2}mr^2\times\dfrac{v^2}{r^2}$

$v_{r}^2=2gh$....(I)

We need to calculate the speed of disc at the bottom

Using work energy theorem

$W=\Delta K.E$

$mgh=\dfrac{1}{2}I\omega^2$

$mgh=\dfrac{1}{4}mr^2\times\dfrac{v^2}{r^2}$

$v_{d}^2=4gh$....(II)

Divided equation (I) by equation (II)

$\dfrac{v_{r}^{2}}{v_{d}^2}=\dfrac{2gh}{4gh}$

$\dfrac{v_{r}^{2}}{v_{d}^2}=\dfrac{1}{2}$

$v_{d}=\sqrt{2}v_{r}$

Hence, The speed of disc is √2 times of speed of ring at the bottom of the plane.