A block is released from rest at the top of an inclined plane which later curves into a circular track of radius `r` as shown in figure. Find the minimum height `h` from where it should be released so that it is able to complete the circle.

Options

A. r
B. `2.5` r
C. `1.5` r
D. `0.5` r

Answer

B

Explanation

To loop the loop body should not loose contact with the the track anywhere so,
`vgesqrt(gr)`
Applying law of conservation of mechanical energy between points A and B, i.e., magnitude of change in kinetic energy equals the magnitude of change in potential energy.
`rArr" "(1)/(2)mv^(2)-0=mg(h-2r)`
`(1)/(2)m(sqrt(gr))^(2)=mg(h-2r)rArrh=(5)/(2)r`
Hence, h must be atleast equal to `2.5` r.