Answer:
A)
B)
C)
Explanation:
Given that:
- no. of turns i the coil,  
- area of the coil,  
- time interval of rotation,  
- intensity of magnetic field,  
(A)
Initially the coil area is perpendicular to the magnetic field.
So, magnetic flux is given as:
 ..................................(1)
..................................(1)
  is the angle between the area vector and the magnetic field lines. Area vector is always perpendicular to the area given. In this case area vector is parallel to the magnetic field.
 is the angle between the area vector and the magnetic field lines. Area vector is always perpendicular to the area given. In this case area vector is parallel to the magnetic field.


(B)
In this case the plane area is parallel to the magnetic field i.e. the area vector is perpendicular to the magnetic field.
∴  
From eq. (1)


(C)
According to the Faraday's Law we have:



 
        
             
        
        
        
Answer:
 (for small oscillations)
 (for small oscillations)
Explanation:
The total energy of the pendulum is equal to:

For small oscillations, the equation can be re-arranged into the following form:

Where:
 , measured in radians.
, measured in radians.
If the amplitude of pendulum oscillations is increase by a factor of 4, the angle of oscillation is  and the total energy of the pendulum is:
 and the total energy of the pendulum is:

The factor of change is:


 
        
             
        
        
        
Answer:
Rectangular path
Solution:
As per the question:
Length, a = 4 km
Height, h = 2 km
In order to minimize the cost let us denote the side of the square bottom be 'a'
Thus the area of the bottom of the square, A = 
Let the height of the bin be 'h'
Therefore the total area, 
The cost is:
C = 2sh
Volume of the box, V =  (1)
            (1)
Total cost,  (2)
            (2)
From eqn (1):

Using the above value in eqn (1):


Differentiating the above eqn w.r.t 'a':

For the required solution equating the above eqn to zero:


a = 4
Also

The path in order to minimize the cost must be a rectangle.
 
        
             
        
        
        
Answer:
A regulation game consists of 7 innings unless extended because of a tie score or unless shortened because the home team needs none or only a fraction of its 7th inning or unless 1 team is leading by 10 runs after 5 innings.
Explanation:
 
        
             
        
        
        
Answer
given,
resistance = 0.05 Ω 
internal resistance of battery = 0.01 Ω 
electromotive force = 12 V
a) ohm's law
         V = IR
      and volage
     
 
now, 
     
 
    
     
 
inserting the values
     
 
       I = 200 A
b) Voltage
    V = I R
    V = 200 x 0.05
    V = 10 V
c) Power 
     P = I V
     P = 200 x 10 = 2000 W
d) total resistance = 0.05 + 0.09 = 0.14 Ω
   
 
     
 
      I = 80 A
      V = 80 x 0.05 = 4 V
      P = 4 x 80 = 320 W