Question

If the mass of a ring which is 5 m wide is 15kg, find its mass per meter.

Answer 1

Answer:

Correct option is

C

2.52mm

Mass (m)=15 kg

Length of wire (L)=1 m

Area of cross section of wire (A)=0.05cm²=5×10

−6

m

2

Angular frequency (ν)=2 rev/s

So, Angular velocity, (ω)=2πν=2π(2)=4π rad/s

Young's modulus for steel (Y)=2×10

11

N/m

2

At the lowest point of the vertical circle,

T−mg=mω

2

L

T=mg+mω

2

L

=15[9.8+(4π)²×1]

=15(9.8+16π²)

=15×167.72 N

=2515.8 N

Now,

Youngs modulus =

strain

stress

Y=

A∆L

TL

∆L=

AY

FL

=

(5×10

−6

)×(2×10¹¹)

2515.8×1

=2.52×10

−

3 m

ΔL=2.52 mm

Hence, option (C) is correct.