First slide

Torque

Question

A 60 cm metal rod $O A$ is joined to another 100 cm metal rod $O B$ to form an L shaped single piece. This piece is hung on a peg at the joint O . The two rods are observed to be equally inclined to the vertical. If the two rods are equally thick, the ratio of density of $O A$ to that of $O B$ is

Difficult

A

5/3
B

3/5
C

25/9
D

9/25

Solution

For equilibrium, moment of $m_{1}$ g about O = moment of $m_{2}$ g about O ⇒ ( $λ_{1}$ x 60 x g) x 30sinθ = ( $λ_{2}$ x 100 x g) x 50sinθ

$\large \frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{{100 \times 50}}{{60 \times 30}} = \frac{{25}}{9}$

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