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

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

Grade:11

1 Answers

Niloy Mazumder
24 Points
5 years ago

Let’s take VG  is the speed of the center of the ladder .

Instantaneous angular velocity

\omega =\frac{v}{\frac{l}{2}}=\frac{v_{G}}{lsin30}

so v=vG

v=Gv⇒∘30sinlGv=2lv=ω" id="MathJax-Element-38-Frame" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">v=v_{G}ωv=v_{G}=vl2=vGlsin30∘⇒vG=v

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