Q. 52

# Figure (8-E14) sh

The length of the height is given as

Given

The length of the tight rod is given as “l”, the gap between the final and initial position of the ring is given as “h”

Formula Used

The formula for the total energy in terms of kinetic and potential energy is given as

where

The is the total energy in terms of kinetic and potential energy, m is the mass of the object, g is the acceleration in terms of gravity and l is the length of the object.

Explanation

The energy is given as total in form of the static and dynamic form of energy which is

The potential energy of the block is given as

Now equating the equations of energy we find the gap of the final and initial position of the ring that is “h”.

The value of the height can only be minimum if and only if the velocity of the object is nullified meaning the value of the velocity is taken as , Hence, giving the height between final and initial gap of the ring placement as

Hence, the length of the height is given as.

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