The length of a Wire is increased by 16 cm when a weight of 5 kg is hung. If all conditions are the same, what will be the increase in its length when the diameter is doubled?
plss help...
Answers
Answered by
8
Explanation:
156cm² will be the answer
Answered by
9
The increase in length will be 4 cm.
According to the formula of Young's Modulus,
Y = Stress/ Strain
Stress = Force (F)/ Area of cross section (A)
Area of cross section = πd²/4
Where d is the diameter of the wire
Strain = l/L
l = increase in length of the wire
L = Actual length of the wire
Given, a weight of 5 kg is hung.
So, F = 5 g N
So, Y = FL/Al
⇒ Y = 4 FL/πd²l
∴ d²l = constant [∵ Y for a material is same and given, the other conditions are also same]
Suppose the initial diameter is = d
The final diameter is = 2d
The initial increase in length is = 16 cm
Suppose, the final increase in length is = l
∴ d² × 16 = 4d² × l
⇒ l = 4
So, the increase in length will be 4 cm.
Similar questions