A ladder of length L is slipping with its ends against a vertical… - Vidyadip

MCQ

$A$ 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 $\alpha = 30^o$ with the horizontal. Then the speed of the ladder’s center must be

A
$2v / \sqrt 3$
B
$v/2$
✓
$v$
D
None

✓

Answer

Correct option: C.

$v$

c
$\omega=\frac{V}{l / 2}$

$\omega=\frac{2 \mathrm{v}}{l}$

Also, $v_{c}=r \omega=\sqrt{\left(\frac{\sqrt{3}}{4} l\right)^{2}+\left(\frac{l}{4}\right)^{2}} \omega$

$=\frac{1}{4} l \sqrt{3+1} \omega=\frac{l}{2} \omega$

$=\frac{l}{2} \times \frac{2 \mathrm{v}}{l}=\mathrm{v}$

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