E EST INFORMATI O ) & ANOOP (EP) NO. 1

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TARGET : JEE (MAIN)

EE ST

INFORM ATI O

Course : VIJETA (JP) & ANOOP (EP)

PPHHYYSSIICCSS

DPP DPPDPPDAILY PRACTICE PROBLEMS

NO. 1

DPP Syllabus : Kinematics, Newton's Laws of Motion, Friction, WPE.

Revision DPP No. # 1

Total Marks : 300 Max. Time: 180 min. Single correct Objective ('–1' negative marking) Q.1 to Q.60 (4 marks) [240] Integer type Questions (‘0’ negative marking) Q.61 to Q.75 (4 marks) [60]

SECTION - I Straight Objective Type

This section contains 60 multiple choice questions. Each question has 4 choices (1), (2), (3) and (4) for its answer, out of which ONLY ONE is correct.

1. The vertical height of the projectile at time t is given by y = 4t – t2 and the horizontal distance covered is

given by x = 3t. What is the angle of projection with the horizontal? (1) tan–1 3/5 (2) tan–1 4/5 (3) tan–1 4/3 (4) tan–1 3/4

2. A particle is projected from a horizontal floor with speed 10 m/s at an angle 30º with the floor and

striking the floor after sometime. State which is correct. (1) Velocity of particle will be perpendicular to initial direction two seconds after projection. (2) Minimum speed of particle will be 5 m/sec. (3) Displacement of particle after half second will be 35/4 m. (4) None of these 3. There are two inclined planes AO and OB inclined at 45° and 60° respectively with the horizontal as

shown in figure. When a man moves on the inclined plane AO, he observes that the rain drops are falling at 45° with the vertical. When the man moves on the inclined plane OB, he observes that the rain drops are falling vertically downward. Then actual speed of rain w.r.t. ground is :

(1) 5 2m / s (2) 20 3m / s (3) 10 2m / s (4) None of these




4. A car starts from rest & again comes to rest after travelling 200 m in a straight line. If its acceleration

and deacceleration are limited to 10 m/s2 & 20 m/s2 respectively then minimum time the car will take to travel the distance is -

(1) 20 s (2) 10 s (3) 2 15 s (4) 20

3s

5. One car moving on a straight road covers one third of the distance with 20 km/h and the rest with

60 km/h. The average speed of the car is

(1) 40 km/h (2) 80 km/h (3) 2

46 km / h3

(4) 36 km/h

6. The system starts from rest and A attains a velocity of 5 m/s after it has moved 5 m towards right.

Assuming the arrangement to be frictionless every where and pulley & strings to be light, if the constant force F applied on A then find the value of F.

(1) 75 (2) 85 (3) 95 (4) 100 7. A sphere of mass m is held between two smooth inclined walls AB and

AC. The normal reaction between wall AB and sphere is :

(1) 15mg

7 (2)

30mg

7

(3) 10mg

7 (4)

20mg

7

8. A constant force F = m1g / 2 is applied on the block of mass m

2 as shown in figure. The string and the

pulley are light and the surface of the table is smooth. Find the acceleration of m2.

(1) 1

1 2

m g

2(m m ) (2) 2

1 2

m g

2(m m ) (3) 1

1 2

m

2(m m ) (4) 2

1 2

m

2(m m )

9. When forces 1 2 3F ,F ,F

are acting on a particle of mass m, the particle remains in equilibrium. If the force

1F

is now removed then the acceleration of the particle is :

(1) 1F / m

(2) 1–F / m

(3) 2 3F F / m

(4) 2F / m




10. A combination of three blocks is shown in figure is pushed by a horizontal force of 30 N on a frictionless surface. Force exerted by A on B is

(1) 20 N (2) 40 N (3) 80 N (4) 60 N

11. A uniform rope of length lies on a table. If the coefficient of friction is , then the maximum length 1 of

the part of this rope which can overhang from the edge of the table without sliding down is

(1) μ

(2) μ

(3) μ

μ1 (4) μ

μ 1

12. A mass of 1 kg is suspended by a string A. Another string C is

connected to its lower end (see figure). If a sudden jerk is given to C, then : (1) the portion AB of the string will break (2) the portion BC of the string will break (3) none of the strings will break (4) the mass will start rotating

13. The kinetic energy acquired by a body of mass m is travelling some distance s, starting from rest under

the actions of a constant force, is directly proportional to :

(1) m0 (2) m (3) m2 (4) 3

14. The upper half of an inclined plane of inclination is perfectly smooth while the lower half is rough. A

body starting from the rest at top comes back to rest at the bottom if the coefficient of friction for the lower half is given by

(1) = sin (2) = cot (3) = 2 cos (4) = 2 tan 15. A 20 kg body is pushed with just enough force to start it moving across a floor and the same force

continues to act afterwards. The coefficient of static and kinetic friction are 0.6 & 0.2 respectively. The

acceleration of the body is: (1) 6 m/s2 (2) 1 m/s2 (3) 2 m/s2 (4) 4 m/s2

16. A man places a vertical chain (of mass ‘m’ and length ‘’) on a table slowly. Initially the lower end of the

chain just touches the table. The man drops the chain when half of the chain is in vertical position. Then work done by the man in this process is :

(1) – mg 2

(2)

mg–

4

(3)

3mg–

8

(4)

mg–

8

17. Pulling force making an angle to the horizontal is applied on a block of weight W placed ona

horizontal table. If the angle of friction is , then the magnitude of force required to move the body is equal to :

(1) α

θ α

W sin

gtan( ) (2)

α

θ α

W cos

cos( ) (3)

α

θ α

W sin

cos( ) (4)

α

θ α

W tan

sin( )

18. A body is moved along a straight line by a machine delivering constant power. The distance moved by

the body in time t is proportional to : (1) t1/2 (2) t3/4 (3) t3/2 (4) t2




19. The potential energy between two atoms in a molecule is given by U(x) = 12

a

x –

6

b

x ; where a and b

are positive constants and x is the distance between the atoms. The atoms is in stable equilibrium when

(1) 611a

x5b

(2) 6a

x2b

(3) x = 0 (4) 62a

xb

20. An engine pump is used to pump a liquid of density continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is:

(1) 1

2Av3 (2)

1

2 Av2 (3)

1

2 Av (4) Av

21. The component of vector ˆ ˆ2 i 3 j along vector ˆ ˆj 5 i is :

(1) 7

13 (2)

7

26 (3)

13

13 (4) none of these

22. The potential energy function associated with the force 2ˆ ˆF 4xy i 2x j

is :

(1) U = – 2x2 y (2) U = – 2x2 y + constant (3) U = 2x2 y + constant (4) not defined

23. The velocity v of a particel at time t is given by v = at + b

t c, where a, b and c are constants. The

dimensions of a, b and c are respectively :- (1) LT–2, L and T (2) L2, L and LT2 (3) LT2, LT and L (4) L, LT and L2 24. A roller coaster car travels down the helical path at constant speed such that it's parametric coordinates

varies as x = c sin (kt), y = c cos (kt), z = h – bt where c, h, k and b are constants, then the magnitude of it's acceleration is:

(1) 0 (2) ck2 (3) 2 2c k

h (4) bk2

25. The deceleration experienced by a moving motor boat after its engine is cut–off is given by dv

dt = –kv3

(v is velocity) where k is position constant. If v0 is the magnitude of the velocity at cut–off, the magnitude

of the velocity at a time t after the cut–off is :

(1) 0v

2 (2) v

0e–kt (3) 0

20

v

2v kt 1 (4) 0

20

v

2v kt 2

26. A particle moving with uniform acceleration along x-axis has speed v m/s at a position x metre given by

v 180 16 x (0 < x < 180

16). The acceleration of the particle in m/s2 is

(1) –16 (2) – 8 (3) 164 (4) 8

160 16 x




27. A particle starts from rest with uniform acceleration and its velocity after n seconds is v. The displacement of the body in last two seconds is

(1) v(n 1)

n

(2)

2v(n 1)

n

(3)

2v(n 1)

n

(4)

v(n 1)

n

28. A particle moves along x-axis in positive direction. Its acceleration 'a'

is given as a = cx + d, where x denotes the x-coordinate of particle, c and d are positive constants. For velocity-position graph of particle to be of type as shown in figure, the value of speed of particle at x = 0 should be.

(1) 24d

c (2)

2d

c (3)

22d

c (4)

28d

c

29. A particle is moving in a straight line whose acceleration versus time

graph is given. Assume that initial velocity is in the direction of acceleration. Then which of the statement is correct between time t = 0 to t = t

0.

(1) Velocity first increases then decreases, displacement always increases

(2) Velocity and displacement both, first increases and then decreases (3) Displacement increases and velocity decreases (4) Displacement and velocity both always increases 30.

The graph shows the variation of 1

V (where V is the velocity

of the particle) with respect to time. Then find the value of acceleration at t = 3 sec. (1) 3 m/s2 (2) 5 m/s2 (3) 1 m/s2 (4) None of these

31. Velocity versus displacement graph of a particle moving in a straight

line is as shown in figure : The acceleration of the particle is :

(1) constant (2) increases linearly with x (3) increases parabolically with x (4) None of the above

32. A particle is projected from ground level under gravity. It's range v/s projection angle graph is drawn

keeping fixed projection speed. Then time of flight of particle corresponding to maximum height attained by particle is:

(1) 2 5 sec. (2) 2 10 sec. (3) 3 5 sec. (4) 3 10 sec.




33. For ground to ground projectile, time taken by a particle to go from point O to point C is T1 and during

the same motion time taken by the particle to go from A to B is T2, then height 'h' is :

(1) 1

2 gT

12 (2)

1

4g(T

12 – T

22) (3)

1

8 g (T

12 – T

22) (4)

1

8g(T

2– T

1)2

34. A particle is projected from ground from O with speed 20 m/s making an angle 45º with ground. Two

high smooth and vertical walls are present, one 10m ahead and other 15m behind the point of projection. If collision of the particle with the walls are perfectly elastic then where will the particle land from the point of projection ?

(1) 5m ahead (2) 5m behind (3) 10m ahead (4) 10m behind 35. If the angle of projection of a particle from the horizontal is doubled keeping the speed of projection

same the particle strikes the same target on the ground then the ratio of maximum height in the two cases will be :

(1) 1 : 1 (2) 1 : 2 (3) 1 : 3 (4) 1 : 4 36. A platform is pulled with a constant acceleration a. A particle is

projected from the platform at angle with the horizontal with respect to the platform as shown in the figure. The value of tansuch that particle again come to the starting point on the platform is (a = 5 m/s2): use g = 10 m/s2

(1) 4 (2) 6 (3) 2 (4) 3 37. A man standing on a truck moving with a constant acceleration 'a', throws a ball in vertically upward

direction with speed 'v' relative to truck. The minimum speed of the ball observed by the man during the flight will be :

(1) 2 2

va

a g (2)

2 2

vg

a g (3) zero (4) None of these

38. A projectile has same range R for two angles of projection. If t1 & t

2 be the time of flight for the two

cases then :

(1) R = 1 2gt t

2 (2) R =

21 2g(t t )

2

(3) R = 1 2g t t (4) R = 1 2

1 2

t t

t t 2g

39. Two smooth spheres each of radius 5 cm and weight W rest one on the other inside a fixed smooth cylinder of radius 8 cm. The reactions between the spheres and the vertical side of the cylinder are: (1) W/4 & 3W/4 (2) W/4 & W/4 (3) 3W/4 & 3W/4 (4) W & W




40. A block starts from rest at the top of frictionless slide at a height, h1 above the ground. The block leaves the slide moving perfectly horizontally at a height h2 above the ground. The block eventually hits the

ground traveling at an angle = 30° below the horizontal. The ratio of h1 and h2 is

(1) 4

1 (2)

2

5 (3)

4

3 (4)

3

1

41. The acceleration of 8 kg block just after system is released is : (All surfaces are smooth, ideal pulleys,

massless strings) (g = 10 m/s2) 10 kg

7 kg

8 kg 5 kg

(1) 1 m/s2 (2) 2 m/s2 (3) 1.5 m/s2 (4) None of these 42. A motor is fixed inside a box which is moving upwards with

velocity 5 m/s. String is winding at the rate 3 m/s. Then the velocity of block A will be: (1) 2.5 m/s downwards (2) 5 m/s downwards (3) 1 m/s downwards (4) 2 m/s downwards

43. A particle with total mechanical energy, which is small and negative, is under the influence of a one

dimensional potential U(x) = x4/4 – x2/2 J where x is in meters. At time t = 0 s, it is at x = – 0.5 m. Then at a later time it can be found.

(1) anywhere on the x axis (2) between x = – 1.0 m to x = 1.0 m (3) between x = – 1.0 m to x = 0.0 m (4) between x = 0.0 m to x = 1.0 m.




44. In the pulley system shown in figure, block C is going up at 2 m/s and block B is going up at 4 m/s, then the velocity of block A on the string shown in figure, is equal to :

(1) 2 m/s (2) 4 m/s (3) 6 m/s (4) 8 m/s 45. Two rods are moving with constant velocity v in perpendicular direction to their length as shown in

figure. The velocity of point of intersection of two rods will be :

(1) v cosec (2) v cos (3) v sin (4) 2vsin 46. In the figure mA = mB = mC = 60 kg. The co-efficient of

friction between C and ground is 0.5, B and ground is 0.3, A & B is 0.4. C is pulling the string with the maximum possible force without moving. Then tension in the string connected to A will be:

(1) 120 N (2) 60 N (3) 100 N (4) zero 47. A body of mass m was slowly hauled up the hill as shown

in figure by a force F which at each point was directed along a tangent to the trajectory. Find the work performed by this force, if the height of the hill is h, the length of its

base , and the coefficient of friction k.

(1) mg h (2) mg (h + k) (3) mg (h – k) (4) None of these

48. A block of mass 4 kg is pressed against the wall by a force of 80N as shown in figure. The value of friction force is

(take s = 0.2) (1) 32 N (upward) (2) 8 N (downward) (3) 8 N (upward) (3) 32 N (downward)

4kg

37°

80N




49. Starting from rest a body slides down a 45º inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The co-efficient of friction between the body and the inclined plane is: (1) 0.75 (2) 0.33 (3) 0.25 (4) 0.80

50. A small mass slides down an inclined plane of inclination with the horizontal. The co-efficient of friction is = 0 x where x is the distance through which the mass slides down and 0, a constant. Then the speed is maximum after the mass covers a distance of

(1) 0

cos

(2) 0

sin

(3) 0

tan

(4) 0

2tan

51. Power of the only force acting on a particle of mass m = 1 kg moving in straight line depends on its velocity as P = v2 where v is in m/s and P is in watt. If initial velocity of the particle is 1 m/s, then the displacement of the particle in ln2 second will be :

(1) (n2 – 1)m (2) (n2)2 m (3) 1 m (4) 2 m 52. The components of a force acting on a particle are varying according to the graphs shown. When the

particle moves from (0, 5, 12) to (4, 20, 0) then the work done by this force is :

(1) 192 J (2) 400/3 J (3) 0 (4) None of these

53 A force F

= k ˆ ˆy i x j , where k is a positive constant, acts on a particle moving in the xy plane.

Starting from the origin, the particle is taken along the positive xaxis to the point (a, 0) and then

parallel to the yaxis to the point (a, a). The total work done by the force on the particle is

(1) 2 ka2 (2) 2 ka2 (3) ka2 (4) ka2

54. The system as shown in the figure is released from rest. The pulley, spring and string are ideal & friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is : (spring constant k = 40 N/m & g = 10 m/s2)

(1) 2m/ s (2) 2 2 m/ s

(3) 2 m/s (4) 4 2m/ s

55. Block A in the figure is released from rest when the extension in the spring is x

0. (x

0 < Mg/k). The maximum downwards

displacement of the block is (ther is no friction) :

(1) 02Mg

2xK

(2) 0Mg

x2K

(3) 02Mg

xK

(4) 02Mg

xK

56. The ratio of work done by the internal forces of a car in order to change its speed from 0 to V to, from V

to 2V is (Assume that the car moves on a horizontal road) - (1) 1 (2) 1/2 (3) 1/3 (4) 1/4




57. A plane is flying with an air speed 10 m/s toward north but suddenly encounters a wind of 10 m/s at 30º north of east. If angle made by new direction of velocity of plane with respect to ground from north

direction is n

then value of n is :

(1) 3 (2) 4 (3) 5 (4) 6 58. A particle of mass 2 kg is moving in a conservative field of force in which potential energy of particle

varies with coordinate x as U(x) = 2

10

4 (x 1) where x is in meters and U is in joules. The particle is

initially at x = 3 and it is projected towards origin with a velocity u. What is the minimum value of u, so that the particle can reach the origin.

(1) 3

2m/s (2)

5

2m/s (3)

7

2m/s (4)

3 3

2m/s

59. The minimum work done by external agent in moving a particle from a point (1,1) to (2,3) in a plane and

in a force field with potential energy U = ( x + y ) is :

(1) 3 (2) – 3 (3) (4) 0

60. If the potential energy of two molecules is given by 6 12

A BU

r r , where A and B are constants and r is

the distance between molecules. At equilibrium position, its potential energy is equal to

(1) 2A

4B (2)

2B

4A (3)

2B

A (4)

2B

4A

SECTION-II : (INTEGER TYPE QUESTIONS)

This section contains Fifteen (15) questions. The answer to each question is NUMERICAL VALUE with

two digit integer and decimal upto two digit.

61. Figure shows a 5 kg ladder hanging from a string that is

connected with a ceiling and is having a spring balance connected in between. A boy of mass 25 kg is climbing up the ladder at acceleration 1 m/s2. Assuming the spring balance and the string to be massless and the spring to show a constant reading, the reading (in kg) of the spring balance is : (Take g = 10 m/s2)

62. A force ˆ ˆF (5i 3 j) newton is applied over a particle which displaces it from its origin to the point

ˆ ˆr (2i 1j) metres. The work done (in Jule) on the particle is :

63. A 1 kg block is being pushed against a wall by a force F = 75 N as shown in the Figure. The coefficient of friction is 0.25. The magnitude of acceleration (in m/s2) of the block is:




64. A system is shown in the figure. Block A moves with velocity 10 m/s. The speed (in m/s) of the mass B will be:

65. The potential energy of a certain spring when stretched through a distance 'S' is 10 joule. The amount of work (in joule) that must be done on this spring to stretch in through an additional distance 'S' will be :

66. Two block A and B placed on a plane surface as shown in the figure. The mass of block A is 100 kg and that of block B is 200 kg. Block A is tied to a stand and block B is pulled by a force F. If the coefficient of friction between the surfaces of A and B is 0.2 and the coefficient of friction between B and the plane is 0.3. If for the motion of B the minimum value of F is 100x Newton then the valule of x is -

B

AF

67. A block of mass 10 kg is released on a fixed wedge inside a cart which is moved with constant velocity 10 m/s towards right. Take initial velocity of block with respect to cart zero. If work done by normal reaction (with respect to ground )on block in two seconds is 10x Jule then the value of x is: (g = 10 m/s2).

68. The engine of a futuristic nuclear powered car for which power and speed can have fantastic values

(say 600 kph) can produce a maximum acceleration of 5 m/s2 and its brakes can produce a maximum retardation of 10 m/s2. The minimum time (in sec) in which a person can reach his workplace, located 1.5 km away from his home using this car is

69. The acceleration–time graph of a particle moving on a straight line is as shown in figure. The velocity of the particle at time t = 0 is 2m/s. If velocity after 2 seconds x/4.2 then the value of x is.

70. A perfect smooth sphere A of mass 2kg is in contact with a rectangular block B of mass 4kg and vertical wall as shown in the figure. All surfaces are smooth. Find normal reaction (in N) by vertcial wall on sphere A.

71. A sphere of radius R is in contact with a wedge. The point of

contact is R/5 from the ground as shown in the figure. Wedge is moving with velocity 20 m/s, then the velocity (in m/s) of the sphere at this instant will be:




72. A system is as shown in the figure. All speeds shown are with respect to ground. Then the speed (in m /s) of Block B with respect to ground is :

73. The rear side of a truck is open and a box of mass 20kg is placed on the truck 4 meters away from the

open end = 0.15 and g = 10m/sec2. The truck starts from rest with an acceleration of 2m/sec2 on a straight road. The box will fall off the truck when it is at a distance (in meter) from the starting point equal to:

74. Find the maximum horizontal force F (in newton) which can

be applied such that sliding does not occur between A and B.

1kg

2kg

µ = 0.5

µ = 0.1

A

B

F

75. Block A has a mass of 2 kg and block B 20 kg. If the

coefficient of kinetic friction between block B and the horizontal surface is 0.1 & B is accelerating towards the right with a = 2 m/s2, then the mass ¼in kga½ of the block C (see the

figure) will be:

ANSWER KEY OF REVISION DPP No. # 1 1. (3) 2. (4) 3. (3) 4. (3) 5. (4) 6. (1) 7. (1) 8. (1) 9. (2) 10. (1) 11. (3) 12. (2) 13. (1) 14. (4) 15. (4) 16. (3) 17. (3) 18. (3) 19. (4) 20. (1) 21. (2) 22. (2) 23. (1) 24. (2) 25. (3) 26. (2) 27. (3) 28. (2) 29. (4) 30. (1) 31. (2) 32. (2) 33. (3) 34. (4) 35. (3) 36. (3) 37. (1) 38. (1) 39. (3) 40. (1) 41. (3) 42. (3) 43. (3) 44. (2) 45. (1) 46. (4) 47. (2) 48. (2) 49. (1) 50. (3) 51. (3) 52. (1) 53 (3) 54. (2) 55. (1) 56. (3) 57. (4) 58. (2) 59. (1) 60. (1) 61. 32.50 62. 13.00 63. 20.00 64. 11.70 65. 30.00 66. 11.00 67. 96.00 68. 30.00 69. 25.20 70. 34.60 71. 15.00 72. 10.00 73. 16.00 74. 24.00 75. 10.50

E EST INFORMATI O ) & ANOOP (EP) NO. 1

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Transcript of E EST INFORMATI O ) & ANOOP (EP) NO. 1