An object of mass `m` is released from rest at a height `h` above the surface of a table. The object slides along the inside of the loop. The loop track consisting of a ramp and a circular loop of radius `R` shown in the figure. Assume that the track is frictionless. When the object is at the top of the circular track it pushes against the track with a force equal to three times its weight. What height was the object dropped from?

Options

A. `3R`
B. `4R`
C. `5R`
D. `6R`

Answer

B

Explanation

`mg(H-2R)=(1)/(2)mv^(2)" "`…(i)
`N+mg=(mv^(2))/(R),` as `N=3mgrArr4g=(v^(2))/(r)" "`…(ii)
Solving equation (i) & (ii) h=2R