Answer:
The value of R is
.
(B) is correct option.
Explanation:
Given that,
In analyzing distances by apply ing the physics of gravitational forces, an astronomer has obtained the expression

We need to calculate this for value of R


So, The nearest option of the value of R is 
Hence, The value of R is
.
Answer:
EMF induced in the loop is 9.4 V
Explanation:
As we know that initial magnetic flux of the loop is given as



As soon as the area of the loop becomes zero the final magnetic flux of the loop is ZERO
Now as per faraday's law of electromagnetic induction the EMF is induced due to rate of change in magnetic flux
so we will have

so we will have


Answer: (1) The resistance increases and the current decreases.
Explanation:
When the temperature of the filament increases, the vibrational energy of the constituent atoms increases which leads to increase in inter-atomic collision. Thus, the resistance would increase. The increases in resistance would obstruct the flow of charges more leading to decrease in the value of the current.
Hence, when the temperature of the filament increase, the resistance increases and current decreases.
Answer:
The force of the car engine.
Explanation:
The work- energy theorem states that the work done on an object is equal to the change in its kinetic energy. Its expression is given by :

Also, W = F.d
Where
F is the force applied by the engine of car
d is the displacement
m is the mass of an object
u is the initial speed
v is the final speed
So, the force of the car engine increased the car’s kinetic energy. Hence, this is the required solution.
Answer:
The magnitude of the rate of change of the child's momentum is 794.11 N.
Explanation:
Given that,
Mass of child = 27 kg
Speed of child in horizontal = 10 m/s
Length = 3.40 m
There is a rate of change of the perpendicular component of momentum.
Centripetal force acts always towards the center.
We need to calculate the magnitude of the rate of change of the child's momentum
Using formula of momentum


Put the value into the formula


Hence, The magnitude of the rate of change of the child's momentum is 794.11 N.