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CDEF is a fixed conducting smooth frame ...

`CDEF` is a fixed conducting smooth frame in vertical plane. A conducting uniform rod `GH` of mass `m` can move vertically and smoothly without losing contact with the frame. `Gh` always remains horizontal and is given velocity `u` upward and released. Taking the acceleration due to gravity as `g` and present other than `R`. Find out the time tasken by the rod to reach the highest point.

Text Solution

Verified by Experts

The correct Answer is:
`(mR)/(B^(2)l^(2))1n((mgR + B^(2)l^(2)u)/(mg R))`
Let `v` be the speed of the rod at any time. Then the equivalent and free body diagrams of rod are shown in . Applying Newton's second law to the rod,
,
`(mdv)/(dt) = -(mg + Bil)`
where `i = (Blv)/(R)`
From equation (i) and (ii)
`(mdv)/(dt) = -(mg + (B^(2)l^(2)v^(2))/(R))`
Integrating over proper limits we get,
`int_(u)^(0)(mdv)/(mg + (B^(2)l^(2)v)/(R)) = int_(0)^(t)-dt`
`rarr` `t = (mR)/(B^(2)l^(2))1n((mgR + B^(2)l^(2)u)/(mgR))`
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