A student skates up a ramp that makes an angle of 30° with the horizontal: JEE Advanced 2020 Physics

A student skates up a ramp that makes an angle 30 degree with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed vo and wants to turn around over a semicircular path xyz radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)
(A) v₀²- 2gh- 1/2 gR
(B) v₀²- 2gh- √3/2 gR
(C) the centripetal force required at points x and z is zero
(D) the centripetal force required is maximum at points x and z

In physics, mechanical energy describes the potential energy and kinetic energy present in the components of a mechanical system.
The conservation of mechanical energy is a principle which states that under certain conditions, the total mechanical energy of a system is constant. This rule does not hold when mechanical energy is converted to other forms, such as chemical, nuclear, or electromagnetic. However, the principle of general conservation of energy is so far an unbroken rule of physics - as far as we know, energy cannot be created or destroyed, only changed in form.

Centripetal force is an accelerating force that acts on any body that revolves around a centre. This force contributes to keeping the body in rotation. This force is always directed towards the centre.

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