A particle of mass `m` is released from a height `H` on a smooth curved surface which ends into a vertical loop of radius `R`, as shown. Choose the correct alernative(s) if `H=2R`.

Options

A. `H =(3R)/(2)`
B. `H = 5R`
C. `H =(5R)/(2)`
D. None of these

Answer

A

Explanation

Force on body at `A = sqrt2 mg`
`implies F = sqrt(F_(g)^(2)) + F_(c)^(2)) implies F_( c) = mg = mv^(2)//R`
`implies v^(2) = gR`
Using energy conserrvation
`mgH = mv^(2)//2 + mgR = 5mgR//2`
`H = 3R//2`