If mass of the bars be m₁ and m₂. Mass m₁ be at the left side and m₂ be attached to right side of the spring.

 

force applied on the system = F on m₁ in the direction left to the spring.

 

So, acceleration in the system = a = F/(m₁+m₂)

 

This frame is accelerated and thus non inertial frame of reference, and in order to apply Newton's laws of motion we apply a pseudo force (m₁a) towards left on the block m₁ and m₂a towards left to the block m₂.

 

We consider the problem from Center of mass frame. In this frame bars move in opposite directions and come to instantaneous rest at some instant. The elongation of the spring will be minimum and maximum at this instant.

 

Let bar m₁ is displaced by a distance x₁ and the bar m₂ by x₂ from the initial positions.

 

Applying energy equation in center of mass frame,

 

T + U = W_ext

 

Here, Wext = work one by the pseudo forces

 

U = Potential energy of the spring = k(x₁ +x₂)²/2

 

T = Kinetic energy = 0

 

W_ext = m₁F(x₁+x₂)/(m₁+m₂),

 

So, k(x₁ +x₂)²/2 = m₁F(x₁+x₂)/(m₁+m₂)

 

or, (x₁+x₂) = 0 or (x₁+x₂) = 2m₁F/k(m₁+m₂)

 

Hence the maximum seperation b/w the bars equals : L + 2m₁F/k(m₁+m₂)

 

The minimum separation corresponds to zero elongation and is equal to L.

 

 

This can easily be explained as there is accleration in the mass bar m₂ as a result of which there is tension in the spring.

Dear aditi,

                 I request u to expand ucm to get your query answered.

ABSOLUTE AND GAUGE PRESSEURE

 

For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure. An example of this is the air pressure in an automobile tire, which might be said to be "220 kPa", but is actually 220 kPa above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa, the absolute pressure in the tire is therefore about 320 kPa. In technical work, this is written "a gauge pressure of 220 kPa". Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)", is permitted.

Gauge pressure is a critical measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluid systems. However, whenever equation-of-state properties such as densities or changes in densities must be calculated, pressures must be expressed in terms of their absolute values.

 

If work function of the metal is W, and the frequency of the falling light should be greater than threshold frequency for Photo electric effect to take place. Say if initially the frequency is f then K.E of electron is

 

K1 = hf - W, where h = planck's constant

 

K2 = 2hf - W

 

So the factor by which kinetic energy increases is given by K2/K1

 

The increase in intensity will not effect the maximum kinetic energy of electrons released from the surface, but will simply increase the no. of electrons released, which will in turn incerease the current. So if intensity is doubled than this increases the photoelectric current by a factor of 2. But we have also increased the frequency twice so I = dq/dt i.e. rate of flow of charge also increases by some factor. Here the resultant factor by which velocity increases is given by (K2/K1) as a result of which the factor by which current increases on doubling the frequency and intensity is given by 2(K2/K1)

The physical significance of definite integral say _a^b f(x).dx  is area between x-axis from a to b and the curve f(x). So for this the function NEED NOT BE CONTINUOUS as it may be discreet or piecewise continuous like greatest integer value function etc. But for indefinite integral the function should be continuous for its analytical evaluation.

        which of the following sets may represent magnitudes of three vectors       adding to zero

a. 2,4,6

b. 4,8,16

c. 1,2,1

 

Solution) Magnitudes of three vectors will add to zero if the addition or subtration or combination of these gives ZERO as explained below:

 

a) 2, 4, 6 This is the set which gives zero when 2 + 4 - 6 is performed. So YES

 

b) 4, 8, 16. No combination of these three will give zero hence NO

 

c) 1, 2, 1 again 1 + 1 - 2 = 0, so this set may represent magnitudes of three vectors adding to zero.

Answer to your second question is:

 

Gravitational constant = G, is a Universal constant and it remains same

 

throughout the universe and thus on moon also the constant is unaltered

 

      G = 6.6742 x 10^-11 N m² kg^-2

Magnitude of gravitational force between earth and 1 kg object on earth's surface is given by

 

F = GM_em/R²

Where, G = gravitational constant

M_{e ⁼}Mass of earth, m = mass of object, R = radius of earth, m = mass of object

 

Also, GM_e/R² = g = 9.8m/s²

So, F = mg = 1*9.8 = 9.8 N which is the gravitational force on object and same force is exerted by obect on earth (Newton's third law)

Dear Nilesh, thank you very much for the effort you have made, I appriciate your effort and at the same time would like to thank administrator and moderator that they made avialable the very much required figure. i have tried to give possible approach. Please use the following link

 

 

 

 

 

 

 

 

 

Solution to your second problem is explained below:

 

If A  B = A  C and A  B = A  C.

To Prove that B=C.

 

We know that

n(A  B) =  nA + nB - n(A  B)..............(1)

 

Similarly,

n(A  C) =  nA + nC - n(A  C)..............(2)

 

LHS of eqns. (1) and (2) are equal thus equating their RHS's we have

 

nA + nB - n(A  B) =  nA + nC - n(A  C)

 

or nA + nB  =  nA + nC          [as (A  B) = A  C) ]

 

or B = C