Question

A cylinder of mass m and radius r rolls on an inclined plane the gain in kinetic energy is
1. 1/2mv2
2. 1/2iw2
3. 3/4mv2
4. 3/4iw2

Answer 1

Energy of a rotating body is 1/2IW2

Answer 2

Given that,

When an object rolls on an inclined plane, then the total energy is equal to the sum of rotational kinetic energy and translational kinetic energy such that,

$E=\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2$

To find,

The gain in kinetic energy.

Solution,

I is moment of inertia of cylinder, $I=\dfrac{mr^2}{2}$

$\omega=\dfrac{v}{r}$ is angular speed

$E=\dfrac{1}{2}mv^2+\dfrac{1}{2}\dfrac{mr^2}{2}(\dfrac{v}{r})^2\\\\E=\dfrac{1}{2}mv^2+\dfrac{1}{4}mv^2\\\\E=\dfrac{3}{4}mv^2$

So, the gain in kinetic energy is $\dfrac{3}{4}mv^2$. Hence, the correct option is (3).

Learn more,

A cylinder of mass m and radius r rolls on an inclined plane the gain in kinetic energy is?

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