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## Polarisation – Malus Law

Two polariods P1 and P2 are placed with their pass axes perpendicular to each other. Unpolarised light of intensity Io is incident on P1. A third polariod P3 is kept between P1 and P2 such that its pass axis makes an angle of 30 with that of P1. Determine the intensity of light transmitted through P1,P2 and P3.

Appply Malus’ Law

The intensity of light from the first polaroid P1 is Io/2

From P3, the intensity is (Io/2) cos230 =(Io/2)(3/4)=3Io/8

From P2, the intensity is (3Io/8)cos260= (3Io/8)(1/4)= 3Io/32

## Buoyancy

A pound coin floating in mercury (Photo credit: Wikipedia)

I read in one of my chapters that when a body is immersed in a container of water (kept on a weighing machine which  reads ‘W’ at first )the apparent weight lost by the body is equal to the buoyant force, and thus the reading ‘W’ increases.

Then I came across a question like this –

A beaker containing water kept on a weighing machine weighs W. A body of weight  ‘w’ is dropped in it. It is floating & experiencing a buoyant force B, then the reading on machine is –

(a)w+W
(b)W+B
(C)W+w-B
(d)W

the book says answer is (a)
but I think it is (c)

(Anwesha posted this questions)

The total force acting downwards is W+w and the weighing scale is providing an equal reaction. the normal reaction offered by the weighing scale is what we get as the reading.

therefore the reading on the weighing scale must be W+w

The buoyant force is acting on the object dropped and is not contributing to the normal reaction offered by the weighing scale.

## Question from Special Relativity

A spacecraft starts from earth moving at constant speed to planet A which is 20 light-hour away from Earth.

It takes 25 hour (according to an earth observer) for a spacecraft to reach this planet. Assuming that clocks are synchronized at the beginning of the journey, compare the time elapsed in the spacecraft frame for this one-way journey with the time elapsed as measured by an earth-based clock?

Posted by Mona

## Physics Numerical Problems posted by Nabeela

The following questions were posted by Nabeela. We are just posting the question as such so that the visitors can post the answers.

1. A mass-less string pulls a mass of 20kg upward against gravity. The string would break if subjected to a tension greater than 400N. What is the maximum acceleration with which the mass can be moved upward?
2. A bullet of mass 20g is fired from a gun of mass 10kg with a velocity of 180m/s. Find the velocity of recoil of the gun. Find the force required to stop the gun before it moves 20cm
3. A body of mass 40kg is moving up an inclined plane with a uniform velocity when a force of 460N is applied. If the plane is inclined to the horizontal by an angle of 45o,calculate the coefficient of kinetic friction between the surfaces.
4. If the coefficient of friction between the tyres of a truck and the road is k, show that the maximum stopping distance of the truck when moving with a velocity ‘v’ is v2/2 kg. Assume that the brakes are not applied
5. A ball of mass 0.5kg moving with a speed of 20m/s collides with an identical ball at rest. After collision the direction of each ball makes an angle of 30o with the original direction. Find the speed of each ball after collision.
6. What is the maximum horizontal distance that a ball thrown with a speed of 60 m/s can go without hitting the roof of a long hall 30m high?
7. A ball is thrown horizontally strikes a wall 5m away. The height of the point struck by the ball is 1m lower than the height which it was thrown from. (1) With what velocity was it thrown (2) At what angle did the ball reach the wall?
8. The time of flight of aprojectile is 10 seconds . its range on a horizontal plane is 100m . Calculate the angle of projection and the velocity of projection.

## A doubt from Dimensional Analysis

st=u+0.5a(2t-1), both dimensionally or any other

The equation refers to the displacement in the tth second and hence it should have the dimensions of speed; since it is the displacement in one second.

Under this consideration, the equation is dimensionally and otherwise correct.

## A Numerical problem from electricity

In the given diagram,the cell and the ammeter, both have negligible resistance. the resisitors are identical. With switch K open , the ammeter reads 0.6 A. What will be the ammeter reading when the switch is closed?

When the switch is open, the effective resistance is R/2, since the two resistances R each are in parallel.

Therefore, the pd, V = I x R/2 = 0.6 x R/2 = 0.3 R

When the key is closed, the effective resistance becomes R/3

Now the reading of the ammeter, I’ = V/(R/3) = 0.3R/(R/3)=0.9A

## Work done in accelerating a proton

The mass of a proton is 1840 times that of an electron. it is accelerated to a potential difference of 1kV. find the amount of work done in process. (Ujjwal Sharma asked)

The work done = the KE acquired = eV=1.6 x 10-19 x 1000 = 1.6 x 10-16 J

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