A rod of length l is hinged at one end and kept horizontal. It is allowed to fall. The velocity of the other end of the rod is

Question

A rod of length l is hinged at one end and kept horizontal. It is allowed to fall. The velocity of the other end of the rod is (A) √3 g l (B) √2 g l (C) 2 Ml 2 (D) None of these

Tardigrade Admin · Accepted Answer

As the mass is concentrated at the centre of the rod, therefore,

m g \times \frac{l}{2} = \frac{1}{2} l ω^{2} = \frac{1}{2} (\frac{m l ^{2}}{3}) ω^{2}

\Rightarrow ω = \frac{3 g}{l}

Velocity of other end of the rod

v = ω l = 3 g l

Q. A rod of length $l$ is hinged at one end and kept horizontal. It is allowed to fall. The velocity of the other end of the rod is

$3 g l$

$2 g l$

$2 M l^{2}$

None of these

As the mass is concentrated at the centre of the rod, therefore,
$m g \times \frac{l}{2} = \frac{1}{2} l ω^{2} = \frac{1}{2} (\frac{m l ^{2}}{3}) ω^{2}$
$\Rightarrow ω = \frac{3 g}{l}$

Velocity of other end of the rod $v = ω l = 3 g l$

Q. A rod of length l is hinged at one end and kept horizontal. It is allowed to fall. The velocity of the other end of the rod is

3gl​

2gl​

2Ml2