A block of mass m is released from rest at a height R above a horizontal surface. The acceleration due to gravity is g. The block slides along the inside of a frictionless circular hoop of radius R.
-Which one of the following expressions gives the speed of the mass at the bottom of the hoop?

Question

A block of mass m is released from rest at a height R above a horizontal surface. The acceleration due to gravity is g. The block slides along the inside of a frictionless circular hoop of radius R.

-Which one of the following expressions gives the speed of the mass at the bottom of the hoop?

Quizplus · Accepted Answer

By conservation of energy, the potential energy at height R will be converted into kinetic energy at the bottom of the hoop. The potential energy of the block at height R is mgh = mgR, where h = R. At the bottom of the hoop, the potential energy is zero, so all the initial potential energy will be converted to kinetic energy.
mgh = (1/2)mv^2
mgR = (1/2)mv^2
v^2 = 2gR
v =sqrt(2gR) 
Therefore, the speed of the mass at the bottom of the hoop is given by v = 2gR. Choice E is the correct answer.

A Block of Mass M Is Released from Rest at a Height