MELUHA INTERNATIONAL SCHOOL...2020/03/29 · MELUHA INTERNATIONAL SCHOOL INDIA SR MPC 29-03-2020...

MELUHA INTERNATIONAL SCHOOL

INDIA SR MPC 29-03-2020

SECTION – I (SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.

MATHS

SYLLABUS: Matrices (inverse and linear equations), Differentiation

1. If ,A B C then the value of the determinant

2

2

2

sin cot 1sin cot 1sin cot 1

A AD B B

C C is:

A) 1 B) -1 C) 0 D) None of these

2. A divisor of the determinant

2

2

2

11

1

a ab acD ba b bc

ca cb c

is:

A) 2 2 21 a b c B) 2 2 2a b c C) 2a b c D) ab bc ca

3. If , and are the roots of the equation 3 0,x px q then the value of the determinant

A) p B) q C) 2 2p q D) None of these

4. The determinant cos sin cos 2

sin cos sincos sin cos

is:

A) 0 B) Independent of C) Independent of D) Independent of and both

5. The determinant

cos cos coscos cos cossin sin sin

x y y z z xx y y z z xx y y z z x

is:

A) 2sin sin sinx y y z z x B) 2sin sin sinx y y z z x

C) 2cos cos cosx y y z z x D) 2cos cos cosx y y z z x

6. The determinant b c a a

b c a bc c a b

is:

A) 2abc B) 3abc C) 4abc D) None of these

JEE MAINS MODEL

M E L U H A I N T E R N A T I O N A L S C H O O L

Page | 2 MPC :: JEE MAINS MODEL 29-03-2020

7. The set of homogeneous equations 1 1 0tx t y t z , 1 2 0t x ty t z ,

1 2 0t x t y tz has non-trivial solution for: A) Three values of t B) Two values of t C) One value of t D) No value of t

8. If , ,a b c are real then the value of determinant

2

2

2

11 1

1

a ab acab b bcac bc c

if:

A) 0a b c B) 1a b c C) 1a b c D) 0a b c

9. The equation

22 2 2

2

1 2 1 11 1 2

2 1 3 1 5 1 3 2 01 2 2 3 1 2 3 2 2 3

x x xx x x

x x x x x xx x x x x x

A) Has no real solution B) Has 4 real solutions C) Has two real and two non-real solutions D) Has infinite number of solutions, real or non-real 10. The solution of the following equations: 4 3 2 0,x k y z 2 1 1 0,kx k y k z 2 2 3 2 0k x ky k z For 1,k

, ,x y z is given by:

A) ,3 ,t t t B) 2 , 10 , 4t t t C) 9 , 5 , 7t t t D) 4 ,6 ,t t t

11. If 1sin cos2

x y then2

2

d ydx

at ,4 4

is

A) – 4 B) – 2 C) – 6 D) 0

12. If 21t x x and 2 2x t y then at 2, dyxdx

A) 245

B) 101125

C) 488125

D) 358125

13. If 2f x x and g x f f x then 3

0' 2 1

rg r

is equal to

A) 0 B) 1 C) – 1 D) 2

14. If 1yx

then 4 41 1

dy dxy x

A) 0 B) 1 C) x y D) y x

15. If 3

1 txt

and 2

3 42

tyt

then 3'x y

A) 1 'y B) 1 y C) ' 1y D) 'y 16. The value of '' 1y , if 3 2 22 5 5 0x x y x y when 1 1y is equal to

A) 227

B) 21728

C) 8 D) 22827

17. If ' 3 2f then 2 2

2

3 3lim

2x

f h f hh

is

A) 1 B) 2 C) 3 D) 1/2

18. If tan sec 1tan sec 1

x xf xx x

then 'f x is equal to

A) sec tan secx x x B) sec sec tanx x x C) sec sec tanx x x D) None of these



19. If 1 1 costan1 cos

xyx

, then dy

dx is equal to

A) 22sec 2x B) 21 2 sec 2x C) 1 2 D) 21 2 sec 2x

20. 32

4 1

3 1 2 12

x for xf x x x x for x

then

A) f x is continuous at 1x and 4x B) f x is differentiable at 4x

C) f x is continuous and differentiable at 1x D) f x is only continuous at 1x

SECTION-II (Numerical Value Answer Type)

21. Let a b c

A p q rx y z

and suppose that det 2A then the det B equals, where

4 24 24 2

x a pB y b q

z c r

22. Let

2 2

2 2

2 2

1 sin cos 4sin 2sin 1 cos 4sin 2 ,sin cos 1 4sin 2

x x xf x x x x

x x x

then the maximum value of f x is:

23. Let

2

2

cos cos sin sincos sin sin cos

sin cos 0f

then

6f

is:

24. If 1 1 costan ,sin

xy xx

then dydx

25. Let 3 8 7y x x and x f t . If 2dydt

and 3 0x at t then the value of dxdt

at t = 0 _____

SECTION – I

(SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.

PHYSICS

SYLLABUS: Rotational Motion, Gravitation 26. Moment of inertia of solid sphere about its diameter is I. If that sphere is recast into 8

identical small spheres, then the moment of inertia of small sphere about its diameter is:

A) 8I B)

16I C)

24I D)

32I

27. Three particles each of mass ‘m’ are arranged at the corner of an equilateral triangle of side ‘L’. If one of the masses is doubled, the shift in the centre of mass of the system

A) 3

L B) 4 3

L C) 34

L D) 2 3

L



28. A uniform thin bar of mass 6m and length 12L is bent to make a regular hexagon. Its moment of inertia about an axis passing through centre of mass and perpendicular to the plane of the hexagon is:

A) 220 mL B) 26 mL C) 2125

mL D) 230 mL

29. A thin rod of length L and mass M is held vertically with one end on the floor and is allowed to fall. Find the velocity of the other end when it hits the floor, assuming that the end on the floor does not slip

A) 3gL

B) 3gL C) 3Lg

D) 3gL

30. A cylinder of mass M, radius R is resting on a horizontal platform (which is parallel to XY plane) with its axis fixed along the Y axis and free to rotate about its axis. The platform is given a motion in X - direction given by cosx A t . There is no slipping between cylinder and platform. The maximum torque acting on the cylinder during its motion is:

A) 212

MRA B) 2MRA C) 22MRA D) 22 cosMRA wt

31. Find the gravitational attraction on mass m due to the quarter ring of same mass m and Radius ‘R’ as shown in figure.

A)

2

2

2 2GmR

B)

2

22Gm

R C)

2

2Gm

R D)

2

2

2GmR

32. If diameter of a planet is four times that of earth. What is the time period of a pendulum on that planet, if it is a second pendulum on earth. Take mean density of the planet equal to that of earth.

A) 4 sec B) 1 sec C) 2 sec D) 3 sec 33. Two particles of masses 1m and 2m are initially at rest at infinite separation. When released,

what is their relative velocity of approach when they are at a separation d.

A)

1 2( )2

G m md

B)

1 2( )G m md

C)

1 22 ( )G m md

D)

1 22

2 ( )G m md

34. Figure shows a fixed solid sphere of mass M and radius R with a narrow smooth tunnel along its diameter. Another particle of mass m is placed at point A as shown. If the particle is released from rest, then its speed when it reaches the center of sphere is

A)

GMR

B)

2GMR

C) 2

GMR

D) 2 GM

R



35. Two satellites A and B of same mass are orbiting earth at altitudes R and 3R respectively, where R is Radius. The earth taking their orbits to be circular, find the ratio of their kinetic energies.

A) 1 : 3 B) 1 : 1 C) 2 : 1 D) 3 : 1 36. A Satellite of mass 32 10 kg is to be shifted from on orbit of radius 2R to another orbit of

radius 3R. Calculate the minimum energy required for this. [R is the Radius of earth] 210g ms A)

101.066 10 J B) 91.066 10 J C)

102.132 10 J D) 92.132 10 J

37. An artificial satellite is moving in a circular orbit around earth with a speed equal to half the escape Velocity from earth surface. Find the height of satellite above the earth surface.

A) 3200 Km B) 6400 Km C) 10800 Km D) 19600 Km 38. The radius of a planet is 1R and a satellite revolves around it in a circular orbit of

radius 2R .The period of revolution is T. What is the acceleration due to gravity on the surface of the planet?

A)

2 31

2 22

4 RR T

B)

2 31

1

RR T

C)

2 32

2 21

4 RR T

D)

2 31

2 22

RR T

39. A satellite revolves around a planet in an elliptical orbit. Its perigee and apogee are 70.5 10 m and 71.5 10 m respectively. If the minimum speed of satellite in orbit is 35 10 m s , then its maximum speed in orbit is

A) 415 10 m s B) 35 10

3m s C) 41.5 10 m s D) 45 10

3m s

40. The change in the value of ‘g’ at a height ‘h’ above the surface of earth is same as at a depth ‘d’ below the surface of earth. When both ‘d’ and ‘h’ are much smaller than the radius of earth, then which one of the following is correct?

A) 2

hd

B)

32hd

C) 2d h D) d h

41. The distance of the centres of moon and earth is d. The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitional field will be zero.

A) 2d

B)

23d

C)

43d

D)

910

d

42. A point P lies on the axis of a ring of mass M and radius R at a distance R from its centre. A small particle starts from p and reaches the centre under gravitational attraction only. It’s speed at center will be

A)

2GMR

B)

2 112

GMR

C) Zero D)

GMR

43. The gravitational field in a region is given by (4 )E i j N Kg . Work done by this field is Zero when a particle is moved along the line is

A) 4 2y x B) 4 6y x C) 5x y D) All of these 44. Two masses 90 Kg and 160 Kg are at a distance 5 m apart. Find the magnitude of intensity of

the gravitational field at a point which is at a distance 3 m from 90 Kg and 4 m from 160 Kg mass.

A) 110 2 G N Kg B) 110 G N Kg C) 17 G N Kg D) 12 G N Kg 45. Find the height from the earth’s surface where acceleration due to gravity is 25% of it’s value

on the surface of earth. [R=6400Km] A) 3200 Km B) 6400 Km C) 10800 Km D) 19600 Km



SECTION- II (Numerical Value Answer Type)

46. Two kids weighing 10 kg and 15 kg respectively, are trying to balance a see saw of total length

5.00 m, with it’s fulcrum at the centre. If one of the kids is sitting at an end, then what is the distance in meter from the fulcrum to the other kid _____

47. A small hole is made in a disc of mass M and radius R at a distance4R from center. The is

supported on supported on a horizontal peg through this hole. The moment of inertia of the

disc about the peg is 9a

.The value of a is _____

48. A force of 490 N acts tangentially at the highest point of a sphere of mass 5 kg kept on a horizontal plane. If the sphere rolls without slipping, then the acceleration of center of sphere in 2/m s is _____

49. A solid sphere is projected up along an inclined plane of inclination 030 with a speed 12V ms .If it rolls without slipping, then the maximum distance traversed by it in m is 2( 10 )g ms

50. A child is standing with folded hands at the center of a platform rotating about is central axis. The K.E of the system is K. The child now stretches his arms so that the moment of inertia of the system doubles. The K.E of the system is now BK. The value of B is _____

SECTION – I (SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.

CHEMISTRY

SYLLABUS: I-A, II-A, III-A &IV-A Groups, Junior organic Chemistry (GOC) and Alkanes 51. Find out ‘Z’ in the following sequence of reaction Maisture in airAir CuNa x y z 1) 2 3Na CO 2) NaOH 3) 2 2Na O 4) 2Na O 52. Aluminum reacts with NaOH and forms compound ‘X’ If the co-ordination number of Al in

‘X’ is 6,the correct formula, of X is 1) 2 4 2

Al H O OH

2) 2 3 3Al H O OH 3) 2 2 4

Al H O OH

4) 2 6 3Al H O OH

53. Amongst 2, ,LiCl RbCl BeCl and 2MgCl the compounds with the greatest and the least ionic character, respectively are :

1) LiCl and RbCl 2) 2RbCl and BeCl 3) 2 2MgCl and BeCl 4) 2RbCl and MgCl 54. Magnesium burns in air giving two products. Their forumulae are 1) ,MgO MgN 2) 2 3 2,MgO Mg N 3) 3 2,MgO Mg N 4) 2 3 2,Mg O Mg N 55. A piece of magnesium is burnt in air to give ash. Then ash is dissolved in water to liberated a

colorless gas, which turns red litmus to blue.The colorless gas is 1) 3NH 2) 2NO 3) 2N 4) NO 56. Sedimentary rocks laid down under water mainly contain 1) CaO 2) 2Ca OH 3) 3CaCO 4) 4CaSO



57. The property not associated with refractory nature of Mg is 1) it has high m.p 2) it is a good conductor of heat 3) it is chemically inert as well as electrical insulator 4) forms Grignard’s reagent 58. 3 4 3BCl LiAIH A LiCI AICI Re

2 2, .d heatA H O B H B C In this raction sequence A,B and C compounds respectively are

1) 2 6 2 2, ,B H B O B 2) 2 6 3 3 2 3, ,B H H BO B O 3) 2 6 3 3, ,B H H BO B 4) 4, 3 3 2 3,HBF H BO B O 59. Which amongst the following is also called as a sesqui oxide 1) 2 3B O 2) 2 3Al O 3) 2 3Tl O 4) all 60. Which of the following is a lewis acid 1) 3AlCl 2) 2MgCl 3) 2CaCl 4) 2BaCl 61. Silica reacts with hydride of super halogen to form.’X’ on hydrolysis of X another compound

Y on heating to form Z.The ‘Z’ can also be prepared in the following reaction. 1) 2 4 24 2SiO HF SiF H O 2) 2 2Si O SiO 3) 2 6 4 6K SiF K KF Si 4) 2 2 3 22 2Si NaOH H O Na SiO H O 62. Which glass has the highest percentage of lead? 1) Soda glass 2) Flint glass 3) Jena glass 4) Payrex glass 63. Addition of sodium hydroxide solution to a weak acid (HA) results in a buffer of HP is 6. If

ionisation constant of HA is 510 ,the ratio of salt to acid concentration in the buffer solution will be

1) 5:4 2) 1:10 3) 4:5 4) 10:1 64. Decreasing order of ‘P’ Character in the following A : 2 2; : ; :SiO B CO C Graphite 1) A B C 2) B A C 3) B C A 4) A C B 65. The difference in properties of 4CH and 4SiH is due to 1) Large difference in the electronegativity of carbon and silicon 2) Less difference in the size of carbon and Silicon atoms 3) The inability of carbon to expand its octet 4) The inability of silicon to form double bonds 66. The IUPAC name of the alkane is

is 1) 2- Isopropyl-2, 6, 6-trimethylheptane 2) 5 tert-butyl-2isopropyl-2-methypentane 3) 2, 3, 3, 7, 7-Pentamethyloctane 4) 2, 2, 6, 6, 7-Pentamethyloctane



67. The correct Fischer projection formula of (2R,3R)-2,3-dihydroxy butanoic acid is

68. Among the following, the true property

about

3CH

3C CH

3CH

is

1) non-planar 2) C is sp2-hybridized 3) electrophile can attack C 4) does not undergo hydrolysis 69. Select the most stable carbocation from amongst the following

70. Polarization of electrons in acrolein may be written as

1) 2C H CH C H O

2) 2C H CH C H O

3) 2C H CH C H O

4) 2C H CH C H O

NUMERICAL VALUE QUESTIONS

71. How many of the following elements of I A group as lighter than water (i) Cs (ii) Na (iii) K (iv) Li

72. How many of the following will not give any colour in flame (i) Be (ii) Mg (iii) Na (iv) Li 73. Magnesium oxide when mixed with a saturated solution of magnisium chloride sets to a hard

mass like cement known as “sorel cement”. The composition of Sorel cement is . What is the value of n___

74. On heating calcium ammoniate, ammonia and hydrogen are evolved. How many moles of ammonia are evolved when 1.5 moles of calcium ammoniate are heated___

75. The ratio of copper and tin in bell metal alloy is ______.





KEY SHEET

MATHS

1) 3 2) 1 3) 4 4) 2 5) 2 6) 3 7) 3 8) 4 9) 4 10) 3

11) 1 12) 3 13) 1 14) 1 15) 2 16) 4 17) 1 18) 3 19) 2 20) 1

21) -16 22) 6 23) 1 24) 0.5 25) 0.11

PHYSICS

26) 4 27) 2 28) 1 29) 2 30) 1 31) 1 32) 2 33) 3 34) 2 35) 3 36) 1 37) 2 38) 3 39) 3 40) 3 41) 4 42) 2 43) 1 44) 1 45) 2 46) 1.67 47) 16 48) 140 49) 0.56 50) 0.5

CHEMISTRY

51) 1 52) 3 53) 2 54) 3 55) 1 56) 3 57) 4 58) 2 59) 4 60) 1 61) 2 62) 2 63) 4 64) 4 65) 1 66) 4 67) 2 68) 2 69) 2 70) 4 71) 3 72) 2 73) 5 74) 8 75) 4

JEE MAINS MODEL





HINTS & SOLUTIONS MATHS

1. Use: 3 1 2R R R and 2 2 3R R R 2. Multiply 1R 2y ,a 2R 2y b and 3R 2y c and divide the determinant 2y .abc Now take ,a b and c

common from 1 2,c c and 3.c Now use 1 1 2 3C C C C to get 2 2 2 2 2 2

2 2 2

1 1 11 1

1a b c b b b

c c c

Now use: 1 1 2C C C and 2 2 3C C C to get the value as 1. 3. 3 3 3 3D Suppose given 0 As coefficient of 2 0x

Now, 1 1 1

det 0

4. Directly open 2y 1R to get 2 2cos sin cos 2 1 cos 2 . Which is independent of 5. Expand the determinant using first row and use ,x y A y z B and z x C 0A B C 6. Put 1.a b c 7. D simplifies to 4 2 1 0t 8. Multiply 1R 2y a, 2R 2y 2 and 3R 2y c and divide the determinant 2y .abc Now take ,a b and c

common from 1 2,c c and 3.c Now use 1 1 2 3C C C C to get:

2 2 2 2 2 2

2 2 2

1 1 11 1 1

1a b c b b b

c c c

Now use 1 1 2C C C and 2 2 3C C C We get 2 2 21 1a b c 0a b c 9. 1st two columns of 1st determinant are same as 1st two rows of 2nd. Hence transpose the 2nd. Add the

two determinants and use 1 1 3 0C C C D 10. Put 1k and solve

11. 1sin .cos2

x y

cos .cos sin .sin 0dyx y y xdx

cot .cotdy x ydx

JEE MAINS MODEL



2

2 22 cos .cot cos .cot .d y dyec x y ec y x

dx dx

Now ,

4 4

1dydx

2

2,

4 4

2 1 2 1 1 4d ydx

12. Given

2

22 2

11 1

x dt xtx dx x

32 2

2 24

1 12

1x xdyx t y x

dx x

32 2

32

2 1 1

1

x x xdydx x

13. , 2

2 2 4 , 2 44, 4

x xg x x x x

x x

' 1 ' 1 ' 3 ' 5 1 1 1 1 0g g g g

14. 21dy xdx

4

2 2 24

1 1 1 1 01

ydy dydx dx x x xx

15. dy dtdy

dx dx dt

16. Differentiating the given expression, we get 2 2 23 4 4 . ' 5 ' 0x xy x y y y at 1,x we have 3 4.1.1 4.1.1. ' 5 ' 1 0y y

4 3 ' 1 0 ' 1 4 3y y

Differentiating again, we have 22 2 26 4 8 . ' 8 . ' 4 ' 4 . '' '' 0x y xy y xy y x y x y y y

Putting 1, 1 ' 1 4 3x y and y , we get 4 4 166 4 8 8 4 3 '' 1 03 3 9

y

22'' 1 8.7

y

17. 2 2

20

3 3lim

2y

f h f hh

2

20

3 31 lim2 h

f h fh

1 ' 3 2 2 12

f

18.

2 2

2 2

tan sec 2 tan sec 11 tan sec

x x xf xx x



2 2tan sec 2 tan sec 1 tan sec

2 tanx x x x x

x

Thus 2' sec sec tan sec sec tanf x x x x x x x

19. 2

1 12

2sin 2tan tan tan 2 22cos 2

xy x xx

Hence 12

dydx

20. Since g x x is continuous function and 1 1

lim 3 limh h

f x f x

so far f is a continuous function.

In a particular f is continuous at 1x and 4.x f is clearly not differentia2le at 4x . Since g x x is not differentia2le at 0x . Now

0

1 1' 1 lim

h

f h ff

h

0

3 3lim 1h

hh

3 2

0

1 2 1 1 3 1 1 2 3' 1 lim

h

h h hf

h

3 2 2

0

1 2 1 1 2 3' 1 lim 5 2

h

h h h h hf

h

Hence f is not differentia2le at 1x

21. 4 2

det 4 2 4 2 14 2

x a p x a pB y b q y b q

z c r z c r

8 8x y z a b ca b c p q rp q r x y z

8 2 16 22. Use: 1 1 2R R R and 2 2 3R R R and expand to get 2 4sin 2 .f x x

23. Put 6 and find determinant.

24. 1 1 costansin

xyx

2

12sin

2tan2sin cos

2 2

x

y x x

1tan tan2xy

2 2 2 2x xy x or

25. 3 8 7y x x

23 8dy xdx

0 3t x



23 3 8 19dydx

2 0.105319

dydy dt

dxdxdt

PHYSICS26. 2I MR 3M R 1 3R M

1 3

2 2

1 1

R MR M

2

2 2 2

1 1 1

I M RI M R

2 3

2 2 2

1 1 1

I M MI M M

12 32

II

27.

1 1 2 2 3 3

1 2 3cm

m x m x m xxm m m

And also cmy If one of masses dou2led find ' , 'cm cmx y

2 2' 'cm cm cm cmr x x y y

28. 6 onesideI I

222

612

m Lmr

Where 3r l 220I mL

29. 212 2LMg I

2

212 2 3L MLMg

3gL

V r 3V gL 30. cosx A t

sindxV A tdt

2 cosa A t 2

maxa A max maxT I



maxaIR

2

212

AMRR

2max

12

T MAR

31. Mass of element of ring

2mdm d

Force on ‘m’ due to dm

2

2

2

2

GmdmdFR

Gm ddFR

Net force on m will 2e

4

4

cosF dF

2

2

2 2GmFR

32. 3

2 2

43

G RGMgR R

43

g G R

g R 1 2 2

2 1 1

1

2 1

2

1

2 4

1sec

Tg

T g RT g R

RT RT ond

33. At separation ’d’

2 2 1 21 1 1 1

1 12 2

Gm mm v m vd

From law of conservation of linear momentum 1 1 2 2m v m v From (1) and (2)

22

11 2

2( )

GMVd m m

and

2

12

1 2

2( )

GMVd m m

Relative velocity 1 2relV V V



34. potential due to sphere at point ,2AGMA V

R

Potential due to sphere at point 3,2c

GMC VR

Work done (1)A CW V V

21 (2)2

W mv

From (1) and (2) 2GMVR

35. Or2ital speed, GMV

R h

Kinetic energy = 212

mv

2

1 1 2

1 2 1

3 4 22 1

KE V R h R R RKE V R h R R R

36. Total energy of a satellite, 2

GMmEr

Work done in shifting, f iW E E

3 3

10

1 12 2 3

1210 6400 10 2 10

121.066 10

GMmWR

gRmW

W

W J

37. Or2it speed 0GMVR h

Given 01 1 22 2e

GMV VR

1 22

1 12

6400

GM GMR h R

R h Rh r Km

38. Time period, 2 3

2 24 RTGM

Acceleration due to gravity

21

GMgR

2ut

2 32

2

2 32

2 21

4

4

RGMT

RgR T

39. From conservation of angular momentum



a pL L 1 1 2 2mrv mr v

7 3

2 21 7

1

1.5 10 5 100.5 10

r vVr

41.5 10 /m s 40. For smaller heights,

21nhg g

R

Change in g, 1 ng g g

= 2hR

At depth d,

1ddg gR

Change in g, 2g g gd

= dR

Given

1 2

2

2

g gh d

R Rd h

41.

22

22

81

9 1

910

e m

m m

GM GMx d xM Mx d x

x d xdx

42. Potential at a distance R

2 2 2p

GM GMVRR R

Potential at the centre

pGMV

R

Work done (1)p CW V V m

And 21 (2)2

W mv

From (1) and (2), 2 112

GMVR



43. Work done on a particle is zero, if force and displacement are perpendicular. 44. Due to 90 Kg, at’p’

1 2

(90) 103

GE G 90kg 5m 160 kg

Due to 160 Kg, 3 m 4 m

2 2

(160) 104

GE G

Resultant field,

2 2 01 2 1 2

1

2 cos90

10 2

E E E E E

E GNKg

45. At a height ‘h’

2

1n

gghR

; 4hgg

2

4 1

2 1

6400

hR

hR

h R Km

46. In rotational equili2rium Torque due to One kid a2out fulcrum = Torque due to other kid a2out fulcrum

1 1 2 2

10 2.5 152.5 2 5 1.67

3 3

m gr m grx

x m

47. From parallel axes theorem

20

2 2

2 2

;4

2 169 9

16

RI I Mr r

MR MRI

MR MRIa

48. acceleration, 107

FaF

2

10 4907 5

140ms

49. From conservation of energy



22

2

22

2

1 12

21 4 175

2 20 5

sin1

Kmv mghR

KVR

hg

h

Distance,

0

sin

sin 307 225 114250.56

hl

h

m

50. Angular momentum is constantss

2

1 2 1

1 1 1

12

1

.21.

2

20.5

LK EI

K EI

KE I IKE I I

KEKE

KE

Date post:	16-May-2020
Category:	Documents
Upload:	others
View:	2 times
Download:	0 times

MELUHA INTERNATIONAL SCHOOL...2020/03/29 · MELUHA INTERNATIONAL SCHOOL INDIA SR MPC 29-03-2020...

Documents