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

Answer:

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

Explanation:

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

So the acceleration of the cylinder is given as

$a = \frac{gsin\theta}{1 + \frac{k^2}{R^2}}$

so we know that

$\frac{k^2}{R^2} = \frac{1}{2}$

so we have

$a = \frac{gsin\theta}{1 + \frac{1}{2}}$

$a = \frac{2}{3}g sin\theta$

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