FIITJEE 37

1.

A tube of small and uniform cross-sectional area containing water (as shown in the figure) which is in ini- --tially at rest. now liquid is released. Find the force act- -ing on fluid particle of mass dm located at P when level -difference reduces to 2 h from 4 h in the limbs A and B.7h -Curved parts are semicircular (Neglect surface tension P -and viscosity) - 3h -- ---< > -6g( dm) 2g(dm) -- 2 < >--- h /  -16  1 (a) (b) --13 13 - - - - < > < > --- ---h/ - -- -- --2g( dm) 2g( dm) 92  1 (c) (d) 13 13

2.

A source of sound initially at rest moves with constant acceleration of 5 m/s2 towards a stationary observer which is at initial distance of 1000 m. If the original frequency is 900 Hz then the frequency detected by the observer at t = 6 sec is (a) 990 Hz (b) > 990 Hz (c) < 990 Hz (d) Indeterminate.

3.

A ray of light is incident on glass sphere

d  3isilvered at other surface . For what what value of h light will emerge out of the sphere in parallel to incident ray (a)6 m (b) 4m R  4 3m (c) 9 m (d )12 m

5.

A current I flows through a parabloidal surface uniformly. The magnetic field due to the parabolioidal at poin P is (a)

 0I 4 r

(b) zero

(c)

 0I 2 R

(d)

h ---------------------------R  4 3m

I





3  0I 2 4 R

There is a thin uniform disc o fradius R and mass per unit area  , in which a hole of radius R/ 2 has been cut out as shown in the figure. Inside the hole a square plate of same mass per unit area  is inserted so tha its corners touch the periphery of the hole. Find centre of mass of the system

R[2  ] (a) 2 3  2

R[1  ] (b) 2 2   1

2 R (c) 2 3  2

3R (d) 2 2   1

O

r

P

y

-----------

4.

>

c

o

x

>

6.

Consider two arbitrary decay equations and amrk the correct alternative (s) given below (i)

230 92

U  n  229 92 U

Given M

(ii)

230 92

U  p  229 91 U

c Uh= 230. 033927 u , M c Uh= 229.03349u. 230 92

229 92

mn = 1.008665 u, mp = 1.007825, 1amu= 931.5 MeV. (a)Only decay (i) is possible (b) Only decay ( ii) is possible (c) Both the decays are possible (d) Neither of the two decays is possible. 7.

The frequency of a sonometer wire is f but when the weights producing tension are completely immersed in water the frequency becomes f /2 and , on immersing the weights in certain liquid the frequency becomes f /3. The specific gravity by of the liquid is (a) 1.320 (b) 1.032 (c) 1.413 (d) 1.185

8.

Two microscope slides are joined end to end with a thin filter paper bit kept at one of the ends between the slides. The angle between the slides is very small and the medium between the slides is air. Then (a) No interference pattern will be formed (b) An interference pattern of non- uniform fringe width will be formed (c) A minima will be formed at end A (d) A maxima will be formed at end A

9.

Slide 2 B

A

air

Slide 1

A car has its centre of mass of height 1/4m. The distance between its tyres is 1 m and its centre of mass is negotiating a turn of radius 10 m. Then (a) If the friction is sufficient to prevent slipping the car will topple for speeds less than 10 2 m/ s. (b) The normal reaction on outer wheel will be more than on the inner wheels. (c) The reaction will be more on inner wheels. (d) The reaction will be more on rear wheels.

Filter papr bit

 

Assertion-Reason Type This section contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 10.

STATEMENT-1 : A bobin of radius r is pulled by R/2 F a horizontal force F as shown in the figure. R > The frictional force will be always greater than F and opposite to F for pure rolling. because STATEMENT-2: The tangential acceleration of point of contact of bobin with respect to the ground must be zero. (a) STATEMENT-1: is True, Statement-2 is True: Statement-2 is a correct explanation for Statement-1.

(b) Statement-1 is True, Statement-2 is True: Statement -2 is NOT a correct explanation for Statement -1. (c) Statement-1 is True, Statement-2 A is False. (d) Statement-1 is False, Statement -2 is True. 11.

STATEMENT-1: A particle is projected with a velocity 0.5 gR , from the surface of the earth at an angle of 300 with the vertical (at the point) its velocity at the highest point will be 0.25

gR , because STATEMENT-2:Angular momentum of the particle earth system remains constant. (a) STATEMENT-1: is True, Statement-2 is True: Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is True, Statement-2 is True: Statement -2 is NOT a correct explanation for Statement -1. (c) Statement-1 is True, Statement-2 A is False. (d) Statement-1 is False, Statement -2 is True. 12.

STATEMENT-1: The minimum distance between real object and real image for a convex lens= 4 x focal length because STATEMENT-2: Convex lens always converges light. (a) STATEMENT-1: is True, Statement-2 is True: Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is True, Statement-2 is True: Statement -2 is NOT a correct explanation for Statement -1. (c) Statement-1 is True, Statement-2 A is False. (d) Statement-1 is False, Statement -2 is True.

13.

STATEMENT-1: Due to the relative motion of source and detector along the line joining them. the intensity of sound as received by detector changes. because STATEMENT-2: Intenstiy depends upon displacement amplitude, and is independent of frequency. (a) STATEMENT-1: is True, Statement-2 is True: Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is True, Statement-2 is True: Statement -2 is NOT a correct explanation for Statement -1. (c) Statement-1 is True, Statement-2 A is False. (d) Statement-1 is False, Statement -2 is True.

Linked Comprehension Type This section contains 2 paragraphs P 14-16 and P17-19. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B) ,(C) and (D). Out of which ONLY ONE is correct.

P14-16: Paragraph for Question Nos. 14 to 16 From a tower of height y0 a particle is projected vertically up with a velocity v0 in free space (gravity free). The acceleration y    of particle at an instant is given as a  k ( vxA ) , where v is in- v0  c   stantaneous velocity vector and A is given as A  (  k ) , where y y is the vertical coordinate of particle at that instant. (Take origin as foot of the tower) Answer the following questions. 14.

The speed of particle as a function of time will be (a) v0 + kt (b) v0 + (y/t)-(1/2) at (c) v0 - y/t (d) v0

15.

The maximum height attain by the particle will be (a) y = y 0 (1+ e)

16.

The graph between KE vs time will be KE

KE

KE

y0 (0, 0)

x

>

KE

t t t t P 17-19 : Paragraph for Question Nos. 17 to 19 In the year 1916. Tolman-Steward demonstated through an experiment that free charges in a metal are negative and the charge y a to mass ratio of the free charge was also calculated with the help x > of the experiment. In a simplified model of the experiment, con> < sider a metal rod of length L, which is given a uniform acceleraL tion a along the length of the rod towards the rightward direction. Although in the original experiment a rotation spool was taken. Due to motion of the rod on electric field E is set up in the rod in the steady state. Answer the following questions based on the above passage. 17. If the charges are negative in nature, then which end of the rod is at lower potential? (a) x (b) y (c) neither x, nor y (d) more information required

18.

If the potential difference measured across the ends of the rod is V. Then what is the

ch arg e mass

ratio of the charged particles in the rod? (a) 19.

3La V

(b)

2La V

(c)

La V

 (d) E is required

If the rod is not accelerated and placed in the earths’s gravitaton field g, such that the length of the rod is parallel to the direction of g. What is the potential difference across the ends of the rod in terms of the informations of the previous question? (a) Vg/a (b) Va/g (c) Vg2/a2 (d) Va2/g2

PART-B Matrix-Match Type This section contains 3 questions. Each question contains statements given in two columns whcih have to be matched. statements (A, B, C, D) in column I have to be matched with statements (p,q,r,s) in column II. The answer to these questions have to be appropriately bubbled as illustrated in the following example. If the correct match are A-p, A-s, B-q, B-r, C-p, C-q and D-s then the correctly bubbled 4 x 4 matrix should be as follows: 1.

Two smooth rails are kept on an incloned plane of inclination  . A constant vertical magnetic field B is present A wire is sliding on the rail due to it weight as shown in the figure. Match the variation of current in following case. Column-I Column-II (A) This Sliding wire has resistance R (p) B I only R

t

( B

(B) C

This Sliding wire has capacitor C only

(q)

I

 t

( B

(C) L

If the Sliding wire has Inductor L (r) only

I

t

( (D)

B m, L

If there are two identical induc- (s) tors sliding.

I

L, m

( 2.

t

A parallel beam of light is incident following optical devices. Match the shape of wavefront of all the refracted rays

Column -I (A)

>

Column- II (P)

> (B)

(q)

> >

(C) > >

(D)

>

(r)

(s)

> B A 3.

r1

A battery of emf E is connected across a conductor as shown as one observe from A to B. Match the following

r2 >

0 E Column-I (a) Current (b) Drift velocity of electron (c) Electric field (d) Potential drop across the length

Column-II (p) increases (q) decreases (r) remains same (s) Cannot be determine