7/21/2019 4- Iit-jee Physics Paper II

http://slidepdf.com/reader/full/4-iit-jee-physics-paper-ii 1/3

CIITJ Ltd ., FIITJEE House, 29  – A, Kalu Sara i , Sarvapr i ya Vih ar, New Delh i -110016, Ph 26515949, 26569493, Fax:011-26513942. 

FACULTY RECRUITMENT TEST 

PHYSICS (PAPER 2)C A T E G O R Y -   A

(IIT-JEE)

Time: 1 Hour Maximum Marks: 40

Name:.................................................................................

Subject:…………………………...........................................

Marks:

Ins t ruct ions

* Attempt all questions.

* Paper 2 has Two Parts I and II. Each question of Part I carries 2 marks and eachquestion of part II caries 5 marks.

* Calculators and log tables are not permit ted.

PART –

 I

1. Calculate the amount of energy evolved when eight droplets of mercury (surface tension 0.55 N/m) ofradius 1 mm each combine into one.

2. Two uniform solid cylinders A and B each ofmass 1 kg are connected by a light spring offorce constant 200 N/m at their axles and areplaced on a fixed wedge as shown in thefigure. The coefficient of friction between thewedge and the cylinders is 0.2. Find theangle made by the line AB with thehorizontal, in equilibrium.

A

B

30 60 

3. A ball of mass m falls vertically from a height h and collideswith a block of equal mass m moving horizontally with avelocity v on a surface. The coefficient of kinetic friction

between the block and the surface is k  = 0.2, while thecoefficient of restitution (e) between the ball and the block is0.5. There is no friction acting between the ball and theblock. The velocity of the block just after the collisiondecreases by ____________

v

k = 0.2 

m

m

7/21/2019 4- Iit-jee Physics Paper II

http://slidepdf.com/reader/full/4-iit-jee-physics-paper-ii 2/3

 

C

FACREC- CAT-A(IIT-JEE)-P2-PH-2

FIITJ Ltd ., FIITJEE House, 29  – A, Kalu Sara i , Sarvapr i ya Vih ar, New Delh i -110016, Ph 26515949, 26569493, Fax:011-26513942. 

4. A particle of mass m and charge +q approaches from a very largedistance towards a uniformly charged ring of radius R and charge,mass same as that of particle, with initial velocity v 0 along the axis ofthe ring as shown in the figure. What is the closest distance ofapproach between the ring and the particle? Assume the space to begravity free and frictionless. Smooth 

+q  Ring

5. The resistivity of a certain metal is , using a wire drawing machine, a wire of uniform cross-section ismade out of a volume V of the metal. The wire is shaped in a square loop, which is placed in auniform magnetic field B whose direction is parallel to the loop axis. Find the charge flown throughany cross-section of the wire, when the magnetic field is switched off.

6. One end of an uniform rod of length 1 m is placed in boiling water while its other end is placed in

melting ice. A point P on the rod is maintained at a constant temperature of 800 C. The mass ofsteam produced per second is equal to the mass of ice melted per second. If latent heat of steam is 7times the latent heat of ice. Calculate the distance of P from the steam chamber.

7. A rod ACD bent in shape shown in is moving in the x-y plane with a

velocity ˆvi . The magnetic field in the region is B0x  k̂  as shown in the

figure. What will be the emf induced between points A and D (along the

path ACD) as a function of x coordinate of point A. 45 

C

DA

L

y

x

 B

8. Two coherent point sources S1 and S2 of monochromatic

light of wavelength  = 4500 A are located as shown in

the figure [S1S2  = 3]. A screen which can berepresented by plane z = d. Calculate the number ofdark circular fringes formed on the screen.

S2[0, 0, 3  ]

S1[0, 0, 0]

Z = dscreen

Z

3 

O[0, 0, d]

100

9. A light ray incident along vector ˆ ˆ ˆ2i 4 j 5k  strikes on the x-z plane from medium I of refractive

index 3  and enters into medium II of refractive index 2. Find the value of 2 for which the value of

angle of refraction becomes 90.

10. Consider a hypothetical atom having atomic number z = 2. It has two electrons each having mass m. Assume that both electrons always lie diametrically opposite and nucleus of atom contains twoproton. Assume Bohr model is applicable. Find the radius of first orbit of this atom (upto one decimal

place in pm).2 0

0

2

hgiven 1.65A

me

 

7/21/2019 4- Iit-jee Physics Paper II

http://slidepdf.com/reader/full/4-iit-jee-physics-paper-ii 3/3

 

C

FACREC- CAT-A(IIT-JEE)-P2-PH-3

FIITJ Ltd ., FIITJEE House, 29  – A, Kalu Sara i , Sarvapr i ya Vih ar, New Delh i -110016, Ph 26515949, 26569493, Fax:011-26513942. 

PART  – II

11 A composite spherical shell is made up of two materials having thermalconductivities K and 2K respectively as shown in the figure. Thetemperature at the innermost surface is maintained at T whereas the

temperature at the outermost surface is maintained at 10T. A, B, C and D are four points in the outer material such that AB = BC =CD. Find(a) The effective thermal resistance between the inner surface of the

shell and the outer surface of the shell for the radial heat flow.(b) The net rate of heat flow from the outermost surface to the

innermost surface of the shell.

R

 

B 

2R

 

3R

 

K

2K

C 

A 

D 

10 TT

12. There a cylindrical tank of cross sectional area A resting on a horizontal surface. There is a smallorifice of cross sectional area ‘a’ (a << A) at the bottom lateral surface of it. Initially the tank was filled

with a liquid of density  up to a height of H. Find(a) the speed of the liquid flowing out when the height of the liquid in the tank becomes H/2.(b) the horizontal force required to kept it at rest initially.

13. Two blocks of mass 2 kg and M are at rest on an inclined plane

and are separated by a distance of 6.0 m as shown in figure.

The coefficient of friction between each of the blocks and the

inclined plane is 0.25. The 2 kg block is given a velocity of 10.0

m/s up the inclined plane. It collides with M, comes back and

has a velocity of 1.0 m/s when it reaches its initial position.

6.0 m

M

2 kg

The other block M after the collision moves 0.5 m up and comes to rest. Calculate the coefficient of

restitution between the blocks and the mass of the block M.

[Take sin  = tan  = 0.05 and g = 10 m/s2.]

14. A certain series RC circuit is formed using a resistance R, a capacitor without

dielectric having a capacitance C = 2 F and a battery of emf E = 3 V. The circuit

is completed and it is allowed to attain the steady state. After this, at t = 0, half

the thickness of the capacitor is filled with a dielectric of constant K = 2 as shown

in the figure. The system is again allowed to attain a steady state. What will be

the heat generated (in joule) in the capacitor between t = 0 and t = ?d

d/2

K=2