Question

A wire bent in the form of a square of side 30 cm is bent in the form of a rectangle with length 35 cm find width of the rectangle.
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Answer 1

Explanation:

Radius of a circle, r = 35 cm.

Since the same wire is bent into the form of a square,

Perimeter of the circle = Perimeter of the square

Perimeter of the circle = 2πr units

=2×

7

22

×35cm

P=220cm

Let 'a' be the side of a square.

Perimeter of a square = 4a units

4a = 220

a = 55 cm

∴ Side of the square = 55 cm.

Answer 2

Given that,

Field of induction B1 = 0.8T

Area A1 = (15×5×10-4) m2

Now, the flux

  ϕ1=75×10−4×0.8

 ϕ1=60×10−4Wb

Increases field B2 = 1.4T

Area of square A2 = (10×10×10-4) m2

For square,

Flux

  ϕ2=B2A2

 ϕ2=(1.4×100×10−4)Wb

Change in magnetic flux

  Δϕ=ϕ2−ϕ1

 Δϕ=1.4×100×10−4−0.8×75×10−4

 Δϕ=(140−60)×10−4

 Δϕ=80×10−4Wb

Now, Induced emf is

  e=ΔtΔϕ

 e=0.580×10−4

 e=160×10−4

 e=1.6×10−2,volt

Hence, the e.m.f induced in the frame is e=1.6×