Question

The bobs of masses 5 kg and 15 kg are suspended from a rigid support of length 25 m and 9m respectively. The ratio of their time periods is?​

Answer 1

Answer:

The tension force acting on each wire is the same. Thus, the extension in each case is the same. Since the wires are of the same length, the strain will also be the same.

The relation for Youngs modulus is given as:

Y=

Strain

Stress

=

Strain

(

A

F

)

=

Strain

(

d

2

4F

)

....(i)

Where,

F = Tension force

A = Area of cross-section

d = Diameter of the wire

It can be inferred from equation (i) that Y is proportional to (1/d

2

)

Youngs modulus for iron, Y

1

=190×10

9

Pa

Diameter of the iron wire = d

1

Youngs modulus for copper, Y

2

=120×10

9

Pa

Diameter of the copper wire = d

2

Therefore, the ratio of their diameters is given as:

d

2

d

1

=

Y

1

Y

2

=

190×10

9

120×10

9

=

12

19

=1:1.25