Question

In an experiment, ram is being provided a frictionless inclined track that ends in a circular loop of diameter d.Ram put a body on this track and allows it to slide down this track under gravity from a height of 10 cm.The body is just able to complete the circular track. Whats the diameter of the track?

Answer 1

"At the top of the track, potential energy

PE = mgh

At the bottom of the track, kinetic energy

$KE=\frac {mv^{2}}{2 }$

According to conservation of energy, KE = PE

$\frac { Mv^{ 2 } }{ 2 } =mgh$

$v = \sqrt{2gh}$

we know that to complete a vertical circular track the body should have a velocity at the bottom as, $v = \sqrt{5rg}$

hence,$\sqrt{2gh} = \sqrt{5rg}$

$r=\frac { 2h }{ 5 }$

$r=2\times \frac { 10 }{ 5 } =4$

D = 2r = 8 cm

Hence the diameter of the circular track should be 8 cm."