First slide

Pressure in a fluid-mechanical properties of fluids

Question

A uniform rod OB of length 1 m, cross-sectional area 0.012 m² and relative density 2.0 is free to rotate about O in vertical plane. The rod is held with a horizontal string AB which can withstand a maximum tension of 45 N. The rod and string system is kept in water as shown in figure. The maximum value of angle $α$ which the rod can make with vertical without breaking the string is

Difficult

A

45⁰
B

37⁰
C

53⁰
D

60⁰

Solution

F.B. of rod:
$\begin{matrix} W = (0.012) (1) (2 \times 10^{3}) (10) = 240 N \\ F_{b} = (0.012) (1) (10^{3}) (10) = 120 N \end{matrix}$
Torque about O:
(For equilibrium)
$\begin{array}{l} (240 - 120) (\frac{\sin α}{2}) = 45 (\cos α) \\ \Rightarrow \tan α = \frac{90}{120} = \frac{3}{4} \Rightarrow α = 37^{\circ} \end{array}$

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