Question

A body of mass
1 kg is attached to one
and of a wire and roted in
Horizontal
circle of diameter 40cm what
constant speed of
2 m/s what
of. is the area of cross -
section of the wire if the stress
developed in the wire is
5 X 106
N/m² ?
​

Answer 1

Question:

A body of mass 1 kg is attached to one end of a wire and roted in horizontal circle of diameter 40cm what constant speed of 2 m/s what of is the area of cross - section of the wire if the stress developed in the wire is 5 X 106 N/m² ?

Answer:

m=1kg,d=40cm,v=2m/s,stress S=5*10^(6)N/m^2

r=20cm

When rotating the centripetal force is acting on the mass

F=mv^2/r=4/0.2=20N

Stress developed in the wire=force per unit area

S=F/A

Area of cross section A=F/S

A=20/5*10^(6)=4*(10^(-3))^2=4mm^2

A=4mm^2

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Answer 2

Answer:

The area of the given wire is 2mm.

Explanation:

Since the body is being rotated in horizontal circle with the help of a wire, the body will experience an outward force called centrifugal force which will develop stress in the wire.

$Centrifugal\ force(F)=\frac{mv^{2} }{r}$

$=\frac{1*2^{2} }{0.4 }$  On solving F=10N

Stress developed in the wire is force per unit cross sectional area of the material.

$Stress=\frac{F}{A}$  

$5*10^{6} =\frac{10}{A}$

A=$2*10^{-6}$ m²

Hence, the area of the given wire is 2mm.