Sep 2019 CSAT mock test, Physics I #17

As shown in the picture, two objects $\rm A,~B$ are moving along a frictionless track, passing through height $2h_0$ and $h_0$ with speed $v_0$ and $2v_0$ respectively. At the height $h_0,$ the kinetic energy of $\rm B$ is $4$ times the gravitational potential energy. Section $\rm I,~II$ of the track are a horizontal plane and an inclined plane, respectively, and section $\rm III$ is a horizontal plane with height $4h_0.$ Which of the followings are correct about the situation described above?

(1) $\rm A$ takes $\dfrac{5}{3}$ times longer to pass through $\rm I$ completely than $\rm B$ does.

(2) At $\rm II,$ the height at which the kinetic energy and gravitational potential energy of $\rm A$ are the same is $h_0.$

(3) $\rm B$ has the speed of $v_0$ at $\rm III.$

Assumptions

• The gravitational potential energy at $\rm I$ is $0.$

• The objects move along the same vertical plane.

• The size of the objects are negligible.