AP EAMCET2006PhysicsMechanical Properties of Solids
Two blocks of masses 1 ~kg and 2 ~kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is 2 10^9 ~N / m ^2 . What should be the minimum radius of the wire used if it is not to break ? Take g=10 m / s ^2
Options
- A4.6 10⁻⁵ ~m
- B4.6 10⁻⁶ ~m
- C2.5 10⁻⁶ ~m
- D2.5 10⁻⁵ ~m
Correct answer
A. 4.6 10⁻⁵ ~m
Step-by-step solution
The stress in the wire = tension area of cross - section To avoid breaking, this stress should not exceed the breaking stress. Let the tension in the wire be T . The equations of motion of the two blocks are, T-10=1 a and 20 ~N -T=2 a Eliminating a from these equations, T= ( 40 3 ) N Stress T= ( 40 3 ) r^2 If the minimum radius needed to avoid breaking is r , 2 10^9= ( 40 3 ) r^2 Solving this, r=4.6 10⁻⁵ ~m