Reason: Only insulators can be used as Dielectrics within the capacitors in order to make them function properly.
Reason: The water in the bucket will not fall down only if the upward force acting on the bucket is equal to the downward force. The force acting in the downward direction is the weight of the water and the force acting in the outward direction is the centrifugal force.
So we get the following expression:
mg = mv^2/r
gr = v^2
v = square root (gr)
Use the values in the above equation, you will get
v = 5m/s approx
Ans: Sulphur .
Reason: The detailed explanation of the above question can be found here : Solution
Answer: Increase by 2%
Reason: According to the formula:
g = GM/R2
g is inversely proportional to R2.
So, if R will increase g will decrease and if R will decrease g will increase.
Moreover the change in g will be the twice as compared to R, because g is proportional to R2 . If it had been R^3 the change in g would have been 3 times, if it had been square root R, the change in g would have been 1/2 times to that of R.
So in our case R is decreased by 1%, this shows g should increase by 2%.
There is another procedure of solving this problem by using some maths but that is a lengthy process. Its the shortest and best method i.e solving by analyzing.
Answer: Alpha Particles.
Reason: Here we have to make use of De-broglie's equation:
λ = h/mv
v = h/mλ
This shows velocity is inversely proportional to mass and wavelength, in this case wavelength is same for all so the particle with more mass will have the least velocity.
As alpha particle is the heaviest in above mentioned options so it is the correct ans.
Answer: R/4 ohms
Reason: The detailed Solution of this question can be understood from this picture :
Reason: Kinetic Energy is given by
K.E = 0.5 mv^2
= 0.5v (mv)
= 0.5 v P
where P is the momentum. According to the given data Momentum is increased by 100%, which means the momentum is doubled. According to the above equation K.E is directly proportional to the momentum, so if momentum is doubled the K.E will also be doubled in other words our K.E has become 200%. In case the question was what is the change in K.E, then it would have been 100%. Hope its clear.
Answer: 5 mins
Reason: We are to find out how many half lives are involved in this decay and then divide the total time by the number of half lives to get time of one half life.
In one half life 1/2 of the sample decays and 1/2 is left behind. In next half life 1/4 decays and 3/4 is left behind, in next half life 3/8 decays and 5/8 is left behind. So in our case 3 half lives are involved, therefore one half life will be equal to 5 mins.
Reason: There are many possibilities for this transition,in order to find the maximum possible photons we have to sum them all. Electron can first jump from 5th shell to 4th shell, from 4th shell to 3rd shell, from 3rd shell to 2nd shell and from 2nd to 1st shell.This makes 4 photons.
Another possibility is jump from 5th shell to 3rd shell, from 3rd shell to 2nd shell and then to first shell. In this case. In this case only one new photon is produced i,e from transition from 5th to 3rd. Rest were produced in the last case as well.
Next possibility is that electron can jump from 5th shell to 2nd and then from 2nd shell to 1st. In this case again one distinct photon is produced.
Another possibility is that electron can jump from 5th shell to 1st shell directly. This will produce one photon.
Next possibility is the jumping of electron from 5th shell to 4th shell , from 4th to 2nd and then 1st. This gives one more distinct photon.
Next possibility is the jumping of electron from 5th to 4th and from 4th to 1st. This gives one distinct photon.
Another possibility is the jumping of electron from 5th to 3rd and from 3rd to 1st. This will give one more photon.
These are all the possibilities. Sum these all you will get 10.
Students of Maths can solve this problem using the formula of combination. And for medical students here is the shortcut:
Pair each number with the numbers below it i.e 5 with 4,3,2,1. 4 with 3,2,1 . 3 with 2,1 . And 2 with 1.
I mean this:
54 53 52 51
43 42 41
These all are the distinct photons we got in above possibilities. Add these all you will get the answer equal to 10.
The above lines can be summed up in the figure given below: