Question

Identical marbles are released from the same height on each of the following four frictionless ramps . Compare the speed of the marbles at the end of each ramp. Explain your reasoning

Answer 1

Since there is no friction on the ramp so there is no loss of energy in terms of frictional loss

So here we can use mechanical energy conservation law in this case

so here we will have

$U_i = KE_f$

here we know that

$U_i = mgh$

also we know that

$K_f = \frac{1}{2}mv^2$

now we will have

$mgh = \frac{1}{2}mv^2$

now by solving above equation we have

$v = \sqrt{2gh}$

so here as we know all identical balls are released from same height so all balls must have same speed at the end