A student skates up a ramp that makes an angle 30 ° with the horizontal. He/she starts (as shown in the…

A student skates up a ramp that makes an angle $30°$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed $v_0$ and wants to turn around over a semicircular path $xyz$ of 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)

1. $v_0^2-2gh=\frac{1}{2}gR$
2. $v_0^2-2gh=\frac{\sqrt{3}}{2}gR$
3. the centripetal force required at points $x$ and $z$ is zero
4. the centripetal force required is maximum at points $x$ and $z$

Solution

Asked in: JEE Advanced 2020 (Paper 2)

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