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Two bodies of masses 1 kg and 2 kg are connected by a metal wire as shown in fig.A force of10 Nis applied on the body of mass 2 kg. The breaking stress of metal wire is 2 x 109 N/m2. What should be the minimum radius of the wire used, if it is not to break ?

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a

0.23x 10-4 m

b

4x10-4m

c

5x 10-4 m

d

5.2x 1O-4 m

answer is A.

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Detailed Solution

The free body force diagram is shown in fig. From figure ,F-T=2a and T =1x a=a∴ F-a = 2a or F = 3a or a = F/3Therefore, a =(10 / 3)m/s2Now T=a(10 / 3) Stress =Tπr2 or 2×109=(10/3)3⋅14×r2∴ r2=(10/3)3⋅14×2×109=103×3⋅14×2×109r=103×3⋅14×2×109or r=0⋅23×10−4m

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Two bodies of masses 1 kg and 2 kg are connected by a metal wire as shown in fig.A force of10 Nis applied on the body of mass 2 kg. The breaking stress of metal wire is 2 x 109 N/m2. What should be the minimum radius of the wire used, if it is not to break ?