A ladder of length L is slipping with its ends against a vertical wall and a horizontal floor. At a certain moment, the speed of the end in contact with the horizontal floor is `v` and the ladder makes an angle `theta=30^@` with horizontal. Then, the speed of the ladder's centre of mass must be

Options

A. (a) `sqrt3/2v`
B. (b) `v/2`
C. (c) `v`
D. (d) `2v`

Answer

C

Explanation

Distance `AB=const ant`

`:. "Component of V along AB"`
`="component of v along AB"`
or `V/2=(sqrt3v)/(2)`
or `V=sqrt3v`
Now, `(dx)/(dt)=v`
`(-(dy)/(dt))=V=sqrt3v`
`r_c=x/2hati+y/2hatj`
`:. `v_c=(dr_c)/(dt)=1/2[(dx)/(dt)hati+(dy)/(dt)hatj]`
`=1/2[vhati-sqrt3vhatj]`
`:. |v_c|=[sqrt((1/2)^2)+(sqrt3/2)^2]v=v`