A metallic frame of given dimension has area vector at 60° with external magnetic field as shown. The frame is taken out from the field in 10 seconds. Find arrange emf induced in the frame.

The correct option is 1 V.

Given Data:
From the problem description and the provided diagram, we have:
- Dimensions of the rectangular frame: length = 2.5 m, width = 2 m
- Magnitude of the external magnetic field: $B=4\text{T}$
- Angle between the area vector $\overrightarrow{A}$ and the magnetic field vector $\overrightarrow{B}$: $\theta =60°$
- Time duration to remove the frame from the magnetic field: $\Delta t=10\text{s}$

Step-by-Step Derivation:

Step 1: Calculate the area (A) of the metallic frame
Since the frame is rectangular, its area is given by:
$A=\text{length}\times \text{width}$
$A=2.5\text{m}\times 2\text{m}=5{\text{m}}^2$

Step 2: Calculate the initial magnetic flux (${\Phi }_i$)
The magnetic flux linked with the frame initially is:
${\Phi }_i=BA\cos \left(\theta \right)$
Substituting the given values:
${\Phi }_i=4\times 5\times \cos (60°)$
Since $\cos (60°)=0.5$:
${\Phi }_i=20\times 0.5=10\text{Wb}$

Step 3: Calculate the final magnetic flux (${\Phi }_f$)
Once the frame is completely taken out of the magnetic field, the magnetic field passing through the frame becomes zero, so the final magnetic flux is:
${\Phi }_f=0\text{Wb}$

Step 4: Calculate the average induced electromotive force (emf)
According to Faraday's law of electromagnetic induction, the magnitude of the average induced emf ($e$) is given by:
$e=\frac{\left|\Delta \Phi \right|}{\Delta t}=\frac{|{\Phi }_f-{\Phi }_i|}{\Delta t}$
Substituting the values:
$e=\frac{|0-10|}{10}=\frac{10}{10}=1\text{V}$

Therefore, the average induced emf in the frame is 1 V.