Question

A cylinder rolls down two different inclined planes of the same height but of different inclinations :
(1) In both cases the speed and time of descent will be different
(2) In both cases the speed and time of descent will be same
(3) The speed will be different but time of descent will be same
(4) The time of descent will be different but speed will be same

please answer ASAP

thanks​

Answer 1

Answer:

which chapter........

Answer 2

Given:

A cylinder rolls down two different inclined planes of the same height but of different inclinations.

To find:

What will be the result when a cylinder rolls down two different inclined planes of the same height but of different inclinations?

Explanation:

According to the work-energy theorem:

$\displaystyle \mahbf { mgh = \frac{mv^2}{2} + \frac{ I\omega^2}{2} }\\\\\displaystyle \mahbf {$

But I = moment of inertia of sphere = $\displaystyle \mahbf { 12 mr^2}$

$\displaystyle \mahbf { mgh = \frac{1}{2}mv^2 + \frac{1}{2}12 mr^2\omega^2 \\\\\\\\\displaystyle \mahbf { mgh = \frac{1}{2}mv^2 + \frac{1}{2}12 mv^2$

⇒$\displaystyle \mahbf { v^2 = \frac{2gh}{25}$

Hence the speed of the cylinder is the same.

Acceleration of the body rolling without slipping on the inclined plane is

$\displaystyle \mahbf { a = \frac{gsin\theta}{1+\frac{1}{mr^2} } }$

Hence acceleration is directly proportional to sinθ.

i.e. a ∝ sinθ.

And a = $\frac{v}{t}$

i.e. a ∝ v ∝ $\frac{1}{t}$

So the time will be decent.

Option 4 is correct.