Question

A cylinder and a block are at the top of an inclined ramp. The cylinder rolls down the ramp without slipping; the block falls vertically without friction at the same instant. (a) Which object reaches the bottom first?

Answer 1

we can see that block is accelerating with more acceleration and hence it will reach the bottom first

Step-by-step explanation:

As we know that cylinder is rolling without slipping on the inclined plane

So the acceleration of the cylinder is given as

`a = (gsin\theta)/(1 + (k^2)/(R^2))`

so we know that

`(k^2)/(R^2) = (1)/(2)`

so we have

`a = (gsin\theta)/(1 + (1)/(2))`

`a = (2)/(3)g sin\theta`

Now the acceleration of block which is slipping on the floor

`a = g sin\theta`

so here we can see that block is accelerating with more acceleration and hence it will reach the bottom first