Messages posted by Yagyadutt Mishra

For maximum extension you have to encountered the energy balance !
At the mean postion ...Spring will have maximum velocity and also Potential Energy = 0
But at the maximum extension point spring will have zero velocity and the energy will be potential energy

Suppose maximum extension in the spring is x ...
Then potential energy at maximum extension point is m.g.x
Kinetic energy at mean position 0.5.m . (wx)^2 ( where w = )

=> 0.5 m . k / m . x^2 = m.g.x
=> x = 2mg/k

Hence the maximum extension is 2mg/K

Write the full equation ...then only we can determine :)

Considering ! ...

(x^2-a^2)^2 - (y^2-b^2)^2 =0

the (x^2-a^2)^2 = (y^2-b^2)^2
=> x^2 - a^2 = y^2 -b^2 or x^2 - a^2 = -y^2 +b^2
=> x^2 - y^2 = a^2 - b^2 (Represents an ellipse) or x^2 + y^2 = a^2 + b^2 (Represents a circle)

The equation was basically combined equation of ellipse and circle ..!

Hope it is clear
Regards

Yagya

3^2x + 1 = 3^x + 2 +

Let 3^x = t

t^2 + 1 = t + 2 +

t^2 - t - 1 =

Sqaure both side

(t^2-t-1)^2 = (1-6t + t^2)

t^4 + t^2 + 1 - 2t^2 - 2t^3 - 2t = 1 -6t + t^2
t^4 - 2t^3 - 2t^2 + 4t = 0
t( t^3 - 2t^2 - 2t + 4 ) = 0
t(t-2)(t^2-2) = 0

So t = 0 , t = 2 , t = root(2)

As assumption is t = 3^x

So t = 0 ....x = -infinity (neglected)
t= 2 => 3^x = 2 ... x = ln2 ( with base three )

t = root(2) => 3^x = root(2) => x = -ln2 ( with base three)

I didn't understand it clearly ..! What are u saying ...does alpha particle doesn't possess deviation in magnetic field ??
If yes ..! Then let me tell u ...every charge particle passing through the arena of magnetic field will deviate from the path ..for sure ..!
Even electrons beam get deviated in magnetic field ..unless and until forces on them get balanced by external means ... otherwise there is a deviation always :)

Suppose the buoyant force acting on the mass is F ..!

When there is nothing in the box ...i.e m = 9 kg ...then equation of forces is ..

F - 9g ( gravitational force) = 9g/3 ( acceleration) --------------(1)

let the mass of the sand be m ( which is placed inside the box )

So now the equation become

F - (9+m)g [ changed because mass is changed] = [9+m].g/4 -------(2)

Subtract (1) and (2)

mg = 9g/3 - 9g/4 - 9mg/4

13mg/4 = 9g/12

m = (9x4)/12x13
m = 3/13 kg (Ans)

No it is not a/8 ....it is a ...!

Since the other end of the pulley is fixed on the rigid wall hence the consecutive pulleys will share the same acceleration ..!

....

*cap* is used for power notation ..!

t^2 means ...t square
t^-1 means ... t to the power -1 ..

Since i have assume e^cosx as t so e^-cosx will be equal to (e^cosx )^-1 = t^-1

And the substitute these values in equation again ...   t = t^-1 + 4    and then the solution ..(I am not going to solve this again in the same step)

Logic is ...The assumption ...whenever u feel there can be a quadratic equation after assuming some constant ..go for it...I am highlighting few examples ...

1) sinx^2 + 5cosx + 3 = 0

Here u can assume cosx = t => 1-cos^2x + 5cosx + 3 = 1-t^2 + 5t + 3 = 0
or t^2 -5t - 4 = 0   ( and then further u can solve it ) and after getting the value of t suppose u get ..

t=0.5 and t = -3    ...so in this case t=-3 will be neglected because ...as we have assumed t equals to cosx ..which means t can not be less than -1 and greater 1 ...so definitely t=-3 ..doesn't fall in the range ..!

Hence the acceptable answer is t=0.5 ..

2) ln x + 2/lnx = 4

Now how can u solve this without substituting ....Surely assume lnx = t

t + 2/t = 4   again a quadratic equation and ....blah blah blah..(the same step as i have posted above)

3) 2^cosx + 2^-cosx = 5

Again ....say 2^cosx = t ...and further the same step ..!

I hope it is clear to u now ..

nd i also have problem regarding finding the solutions in trigonometry... hw to solve it?

The only way to master yourself in trigonometry is hard practice ...go for examples ...first ..solve as many as question as u can ..in begining u will find difficult to solve it..don't worry ...solve the same question again and again if u will something illogical in it....don't finish unless u understand the logic and steps completely ..

A.Das Gupta for trigonometry is i guess the best book covering and giving a handful knowledge about the topic...Further when u feel confidence ..Go for standard book like M.Khanna ...and Arihant ..and do some tougher problems too ..!

Good luck

After simpication i guess u will get the following expression ..

cosA ( cosx + cosy + cosz) - sinA ( sinx + siny + sinz) = T

and it is given that cosx + cosy + cosz = 0 = sinx + siny + sinz

So the expression T will always be equal to zero ...!

Is it depend on cosA ..and Sin A ... NO !

So it is clear that ...T is independent of A ...

Now for x , y , z ...it is given that for any value of x y z ...we will have cosx + cosy + cosz = 0 = sinx + siny + sinz

Hence it doesn't depend on x,y,z either ...because whatever b the x , y , z will be ...T always becomes zero ..

Hence option is independent of x,y,z and A

Pi ..is considered as an irrational quantity ..! so 1/pi obviously falls in the catalog of irrationality

Van der Waals Equation

The Van der Waals equation is an equation similar to the Real Gas Law, but includes two constants, a and b, to account for deviations from ideal behavior.

The van der Waals equation is:

[P + (n2a/V2)](V - nb) = nRT

Where:

P - pressure,
V - volume,
n - number of moles,
T - temperature,
R - ideal gas constant. If the units of P, V, n and T are atm, L, mol and K, respectively, the value of R is 0.0821
a and b - constants, which are chosen to fit experiment as closely as possible to individual gas molecule.

When the volume, temperature and the number of moles of the gas molecule are known, the pressure can be calculated:

P = [nRT/(V - nb)] - n2a/V2

To calculate Volume:

To calculate the volume of a real gas, V in term n2a/V2 can be approximated as: nR/TP

as ideal gas. Then, V can be calculated as:

V = nR3T3/(PR2T2+aP2) + nb

The van der Waals constants a and b of molecular N2 is 1.390000 and 0.039100, respectively.

To calculate Pressure:

According to the van der Waals equation,

P = nRT/(V - nb) - n2a/V2

Significance of \a/ and \b/ :

1) a measures the force of attraction between the molecules ..

2) b measure the incompressible volume of the molecules ..i.e ( the average volume excluded from the v volume of particle ) = nb and is subtracted by total volume v from the equation ...!

The main point that these constant impacts that ... In case of real gas ...the pressure is not same ..and the volume will also be not same ...Due to inter attraction and intra attraction of the molecules the pressure will increase ....and thus n^2.a/V^2
is added in the original pressure P ...and similarly to compressibility factor ..the actual volume is also not same ...and is decreased by some factor ..that factor is governed by b ..and thus volume become ( V-nb)

So ( effected pressure)(decreased volume ) = nRT

[ P + n^2.a/v^2 ] [ V-nb] = nRT

I hope now it is clear ...! If u have doubts ..ask further

Well if a function is in this format ...f(x) / g(x)

Then there are few steps which u can choose to solve ..!

1) first check whether   f(x) = d(g(x) ...if yes then it become more easy to solve ..

Just choose g(x) = t   => dt/dx = d(g(x) = f(x) and dt = f(x).dx

So integeration will change to    1/ t . dt   and then it can be easily solve ..

2) If f(x) and g(x) are polynomial with degree of g(x) less than f(x) ..then divide f(x) by g(x) .. and integrate it again ...it will become easy ..

3) If f(x) and g(x) are in surds for ...then rationalise it and then integrate ..!

Simplification can always make a problem easier to solve ...

Can't view the image ..upload it again ..i can help then

I guess the graph is clear to ..if not ask further ..!

Our aim is just to calculate the area of shaded portion and multiply it with four ..! That wiill giv the total area bounded in the overlape figure ...

And the shaded portion has area equal to A = ( it is dx after lnx in the integral not x ..sorry editor has some problem)

Which is equal to A = 1(ln1) - 1 - 0 - 0

Taking mod of A (Area never comes positive ) ...so A = 1 unit ..

Hence the area of overlape figure is equal to 4 unit ..!

Okay so 2 must be multiplied ...! and hence the answer would be (C) correct !

A little bit weaker in chemistry so ...! Hope u won't mind

What kind of fun is going out here ..! Can i join too ! :D --

BE = 243 kJ/mole
Since in mole we have 2 Cl atom and for bonding two atom is required ..so there is no need to get confused whether it should be multiplied by 2(mole) or not ...! BE used in calculation will be 243 kJ

Now since this much energy must be carried out by the light which is used for breaking the bonds ..

So light energy hc/lambda = 243 x 10^3 Joule

(12400 x 1.6 x 10 ^-19 J ) x 10^10 = [243 X 10 ^3 J ] X lamda

( hc = 12400 ev/A where ev is electron-volt and A is amstron = 10^-10 ..so when it comes in multiplication become 10^10..unit .. and ev must be converted into joule so multiplied by 1.6x10^-19 )

(After simplification i am getting wavelength ) Lambda = 8164 A ( so i would prefer option A )

Its not likely an electrical device ..
Its an electronics digital device ...!
It inverts the input and produce it as output ..!
Strictly talking about in digital domain ...then If A is the input ....the !A(compliment or inversion of A ) will be produced as output by the inverter ..

Example suppose A = 1 ( input in binary form ..!)
Then Output of Inverter will be = 0

it is ([Force]/[Area])/[ΔVelocity] = [ M L^-1 T ^-1 ]

Hello sir !
Good Afternoon !

1) There should be an edit and delete option for every posted answer ( and should be visible to the owner of that answer)...so that we shouldn't have to post the correct answer again and again...just we click on edit..and we change the correction in the same answer ...or we delete it if necessary ..

2) If possible can u include some mathematicle figure like circle , trianlge , straight line ...or pencil ( as in MS paint) ..so that if we have to include a figure or if we have to solve a question belonging to co-ordinate geometry then it will be uselful ....

3) In the older version i have seen a column in the bottom of site PENDING QUERIES ..is it possible to include it again in the new version ...

Hoping for positive considerations :)
Thanks

Suppose a and b are two vectors inclined at an angle of k with each other ...then the angle of the resultant with the a vecor (z) is given as tan(z) = bsink/[a+bcosk] ( I have take a as P and b as 2P and since resultant angle is same so equated the expression of tan(z) by substituting the a and b )

2Psink / [ P + 2Pcosk ] = (2P+10)sink/[2P + (2P+10)cosK]

2P [ 2P + (2P + 10)cosk] = (2P + 10) [ P + 2P cosk]
4P + 4P.cosk + 20.cosk = 2P + 4P.cosk + 10 + 20cosk
2P = 10
P = 5 (Ans)

Ask if u have any doubts

Van der Waals Equation

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