Question

A Rod is kept vertical as shown in figure, bottom point is stationary. It is allowed to fall. Calculate the velocity of its upper end when it hit the floor.
(Length of Rod $=2m$)
(Mass of Rod $=1kg$)

• A. $\sqrt{40}m/s$
• B. $\sqrt{50}m/s$
• C. $\sqrt{60}m/s$
• D. $\sqrt{70}m/s$

Answer 1

The correct option is C $\sqrt{60}m/s$

In this process mechanical energy will be conserved

Loss in P.E = Gain in K.E

$mgh=\frac{1}{2}I{\omega }^2$

$(1\times 10\times 1)=\frac{1}{2}\left(\frac{m{\ell }^2}{3}\right)\times {\left(\frac{v}{\ell }\right)}^2$

$10=\frac{1}{2}\times \frac{1\times v^2}{3}$

$v^2=60$

$v=\sqrt{60}m/s$