Question

At 40°C, a brass wire of 1 mm is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40ºC to 20ºC it regains its original length of 0.2 m. The value of M is close to :
(Coefficient of linear expansion and Young's modulus of brass are 10⁻⁵/ºC and 10¹¹ N/m², respectively; g = 10 ms⁻²)
(A) 0.5 kg (B) 9 kg
(C) 0.9 kg (C) 1.5 kg

Answer 1

Answer:

HELLO!

Explanation:

The correct option is C.

9kg

Answer 2

The value of M is close to :

Given : Radius of brass wire, r = 1mm, Original length, Lo = 0.2 m, Coefficient of linear expansion and Young's modulus of brass are 10⁻⁵/ºC and 10¹¹ N/m², respectively; g = 10 ms⁻², ∆T = 40 - 20 = 20

• We know that, Young modulus, Y

= (F/A) / (∆L/Lo)

∆L / Lo = F / AY

∆L = FLo / AY

• Also, ∆L = Lo×α×∆T

So, Lo×α×∆T = FLo / AY

α×∆T = F / AY

And F = Mg

α×∆T = Mg / AY

• M = α×∆TAY / g

M = 10^-5×20×pi×10^-6×10^11 / 10

•M = 2×pi = 2×3.14 = 6.28 Kg

Closest to 9 Kg

• Hence correct option is B