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thanks a lot for the reply and taking pains to put up the scan.

the figure is perfect, but unfortunately the only thing i have understood from your explanation is that you have tried to conserve momentum.

firstly, your integration doesn't make sense at all. how can you just integrate both sides with time? what does the product of time and momentum give in the question, for you to have multiplied both sides with dt?

secondly, even if the step is right, you have not expressed velocity as a function to integrate it. velocity has just dissappeared in the last step.

thirdly, i haven't understood the logic you applied in taking the limits. what is the relation between the limits you have taken and the time taken during the motion?

thanks again for the reply anyway, but i don't think the problem is so complicated.

the answer is (mh[cot

] )/(m + M)

if you get it, don't forget to explain you did.

wait, check the question again,

2 balls are thrown in 1 second. this means 1 ball will take 1/2 a sec to reach the max height, which is the required time.

ok, i am also having a slight doubt now,

can you explain the concept. do not use back-substitution this time....

the angle of projection should take care of it

i didn't understand man, why do you need initial velocity?

consider the downward motion, when it falls from the height h. the time taken is still the same. here the initial velocity is zero. what is the problem?

the angle of projection should take care vertical component of the initial velocity automatically.

this is one of the basic concepts in mechanics, so please explain the concept along with your answer.

Q) a block of mass m is resting on a smooth prism ( wedge ) having height h, mass M and making an angle

with the horizontal. the prism is resting on a smooth table. calculate the distance moved by the prism when the block reaches the bottom?

i think (b) is the correct option,

since 2 stones are thrown in one second, one stone reaches max height within half second. for the vertical motion of this stone,

h = 1/2 g t²

h = (1/2) (9.8) (1/2)²

this gives h = 1.225

please correct me if i have gone wrong...

hi,

average velocity is ( total distance travelled)/( total time taken for the journey )

here, since everything is given in ratios, i have taken the liberty to assume that the time taken for the initial part of the journey to be 1 sec ( to make things simpler, implying that time taken for the second part is 8 sec and last is again 1 sec )

for the first part ( during inform acceleration ) we can use the relation v = at

=> 60 = a*1 ( since maximum velocity of 60 km/hr is reached at the end of this phase )

therefore, acceleration a = 60

for the same part, distance s₁ = 1/2 at²

therefore distance travelled = 30 m

for the middle portion ( with constant velocity ), time taken = 8 secs ( by given ratio )

therefore, distance travelled s₂ = vt

= (60) (8) = 480 m

for the third part, the distance travelled and the time taken are the same as the first part, decceleration = - accelaration

therefore total distance is = 30 + 480 + 30 = 540 m

total time taken = 1 + 8 + 1 = 10 s

hence average velocity = 540/10 = 54 m/s

this one is a regular, but worth reading yet again :

While visiting

India

, George Bush is invited to tea with Indian
President Abdul Kalam.

He asks Kalam what his leadership philosophy is. He says that, it is to
surround himself with intelligent people.

Bush asks how he knows if they're intelligent.

"I do so by asking them the right questions," says the Kalam. "Allow me
to demonstrate."

Bush watches as Kalam phones Manmohan Singh and says, "Mr. Prime
Minister, please answer this question: your mother has a child, and
your
father has a child, and this child is not your brother or sister. Who
is
it?"

Manmohan immediately responds, "It's me, Sir!"

"Correct. Thank you and good-bye, sir," says the Kalam. He hangs up and
says, "Did you get that, Mr. Bush?" Bush nods: "Yes Mr. President.

Thanks a lot. I'll definitely be using that!" Bush, upon returning to
Washington , decides he'd better put the Condo leeza Rice to the test.

Bush summons her to the White House and says, "Condoleeza, I wonder if
you can answer a question for me."

"Why, of course, sir. What's on your mind?"

Bush poses the question: "Uhh, your mother has a child, and your father
has a child, and this child is not your brother or your sister. Who is
it?"

Rice was puzzled and finally asks, "Can I think about it and get back
to you?" Bush agrees, and Rice leaves. Rice immediately calls a meeting
of senior senators, and they puzzle over the question for several
hours, but nobody can come up with an answer. Finally, in desperation,
Rice
calls Colin Powell and explains the problem.

"Mr. Powell, your mother has a child, and your father has a child, and
this child is not your brother or your sister. Who is it?"

Powell answers immediately, "It's me, of course."

Much relieved, Rice rushes back to the White House, finds George Bush,
and exclaims, "I know the ! answer, sir! I know who it is! It's our
Colin Powell!"

And Bush replies in disgust, "Wrong!!, it's Manmohan Singh!!"

mind if i try?

1.

a) the word length itself implies it is a scalar ( doesn't have direction ) and therefore cannot be associated with vector

b) a plane area can be associated with a vector ( with direction perpendicular to it ) if it is used to calculate some other quantity involving vectors

c) the surface area of a sphere can also be associated with vectors, to calculate flux, etc otherwise i don't think so ( no direction man! )

2) momentum is conserved in both cases. KE is conserved in elastic only because in inelastic collisions, the body tends to get deformed, due to which kinetic energy is lost.

3) if you consider the particles in a fluid, ya, it does apply for all the collisions and energy changes among them which affects the fluid as a whole

thank you sir, i will definitely do that.

ya, i would agree with you about those 2 concepts, but i was trying to generalize the problem.

what if you get a problem based on the newton's rings experiment in optics? or a question based on the kelvins image method in electrostatics? or a question based on average probability in mathematics?

already guys are filling the forum with countless formulae and concepts god knows where they get from. personally i have never seen this stuff anywhere, and that is what scares me.

in one of the B MAT test papers there was a question using a combination of a plano-convex lens and concavo-convex lens. WOW! now i figure this just keeps better and better

.

sir,

while i was doing capacitors from H C Verma, i found that the concepts of spherical and cylindrical capacitors were dealt with in considerable detail, while these are not mentioned in the JEE syllabus.

the JEE syllabus for capacitors is given as follows:

'Capacitance; Parallel plate capacitor with and without di-electrics; Capacitors in series and in parallel; Energy stored in a capacitor.'

as you can see, the concepts of spherical and cylindrical capacitors are not mentioned specifically anywhere.

this sort of ambuousy is posing to be a real problem for me in other topics also; for instance, the Newtons Rings experiment is not mentioned specifically but it is dealt with in some of the coaching institutes that i know. same thing again with spherical and cylindrical waves..........

you see???

please help.

hey anubhav,

i think adinand's concept involves slipping also.

look at it this way : you first give the disc soem torque (ie. spin it) and then place it on the frictionless floor. since there is no friction, the disc will not move forward but keep spinning in its place. now you can impart a horizontal velocity to the disc due to which it will undergo translational motion. if the linear velocity v=r

, then it will seem that the disc is merely rolling.

of course all of this is just an ideal situation

.