PHYSICS
Daily Practice Problems Target IIT ENTRANCE 2014 Class:XI
Q.1
Discussion: 11-12/05/2012
Time: 45 Min.
M.M.: 40
DPP. NO.-4
A curre current nt carry carrying ing coil coil lies in vertic vertical al plane plane contain containing ing NorthNorth-Sout South h direction direction.. A person person looking looking from from west sees anticlockwise current in it. Choose C hoose the diagram that represents given situation. (g represents [3] acceleration due to gravity) N
(A)
N
S
N
S
(B)
(C)
S
N
S
(D) g
g g
g
Note : Q.2
Implies in to the plane of paper,
implies out of the plane of paper
What What is is the the hei heigh ghtt of a ty typica picall 7 sto story ry Buil Buildi ding ng (A) 112 m (B) 70 m (C) 40 m
[3]
(D) 21 m [3]
Q.3
The SI unit unit of le length ngth is base based d on on : (A) the distance from the north pole to the equator along a meridian passing through Paris (B) wavelength of light emitted by Kr 86 (C) a precision meter stick in Paris (D) the speed of light
Q.4
The hour hour hand hand of of a clock clock is 6 cm long. long. The The magni magnitude tude of of the displac displaceme ement nt of the the tip tip of hour hour hand hand [3] between 1:00 pm to 5:00 pm. is : (A) 6 cm
(B) 6 3 cm
(C) 12 cm
(D) 3 3 cm
Q.5
[3] A vector vector of of magnitu magnitude de 20 is added added to to a vector vector of magni magnitude tude 25. The The magni magnitude tude of this this sum might might be: [3] (A) zero (B) 3 (C) 12 (D) 47 (E) 50
Q.6
If the the unit unit of length length be doubled doubled then then the the numeric numerical al value value of of the universal universal gravit gravitation ation constant constant G will [3] become (with respect to present value) (A) double (B) half (C) 8 times (D) 1/8times Paragra Par agraph ph for questi que sti on nos. nos . 7 to 9 A Bull's eye eye student (Target IIT IIT JEE 2012) was given a question quest ion from paper of IIT JEE 2010 after first chapter was finished. The question was beyond his comprehension but teacher assured the student that you can solve this question with your present capability. capabi lity. Kindly justify the faith of teacher. A particle of mass m moves on the x-axis in a potential energy of the form V(x) = kx 2, where k has unit of force per unit length, it performs simple harmonic motion. x is position positi on on x-axis. The corresponding
time period is proportional to
m
, as can be seen easily using dimensional analysis. However, the k motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx 2 and its total energy is such that the particle does not escape to infinity. infinity. Consider 4 a particle of mass m moving on the x-axis. Its potential energy is V(x) = !x ( ! > 0) for | x | near the origin and becomes a constant equal to V 0 for | x | " X0 .
PAGE # 1
Q.7
The acceleration of this particle for | x | =
(A) Q.8
V mX 0
m
(B)
!
[3]
can be expressed by
V
V
(C)
X0
1
m
A
!
A new physical quantity expressed as Q =
(D)
mX0
VX 0 m
–
(C) A
V0
!X 0
log
!
(D)
m
1
!
A
m
[3]
( )m % && ## . The dimensional formula for quantity kX ' 0 $ [3]
Q & ) are respectively : (A) M0L 3T0, M0LT 2 (C) M0L3T0, M0LT 2
(B) ML 1T0, M0L 1T (D) M L T, M 0L 1T1
–
–
–
Q.10
4
For periodic motion of small amplitude A, the time period T of this particle is proportional to (A) A
Q.9
(B)
X0
–
2
–
–
!
Column-I show vector diagram relating three vectors a , b and c . Match the vector equation in [8] column-II, with vector diagram in column-I : !
Column-I
!
Column-II
b
c
(A)
!
(P)
a , (b + c ) * 0
(Q)
b,c * a
(R)
a + b * ,c
(S)
a+b *c
!
!
a
c b
(B) a
!
!
!
b
a
(C)
!
!
!
c
b
(D)
Q.11
a c
!
!
!
If you began walking along one of Earth's lines of longitude and walked until you had changed latitude by 1 minute of arc, you would have walked a "nautical mile". Find the value of 100 nautical miles (in mile) [5] (Take earth's radius = 4050 miles. Round off your answer to nearest integer.
PAGE # 2
PHYSICS
Daily Practice Problems Target IIT ENTRANCE 2014 Class:XI
Q.1
Discussion: 14-15/05/2012
Q.3
M.M.: 43
DPP. NO.-5
In a particular system of unit, if the unit of mass becomes twice & that of time becomes half, then 8 Joules [3] will be written as _______ units of work (A) 16
Q.2
Time: 45 Min.
(B) 1
(C) 4
(D) 64
During a short interval of time the speed v in m/s of an automobile is given by v = at 2 + bt3, where the [3] time t is in seconds. The units of a and b are respectively: 2 4 3 4 2 3 3 4 (A) m · s ; m· s (B) s /m; s /m (C) m/s ; m/s (D) m/s ; m/s (E) m/s4; m/s5
Two forces P and Q are in ratio P : Q = 1 : 2. If their resultant is at an angle tan
1
–
( 1 % & # ' 2 $
& 3 # to vector & 2 # ' $ [3]
P, then angle between P and Q is : (A) tan
1
–
(B) 45°
(C) 30°
(D) 60°
Paragraph for question nos. 4 to 6 You are kidnapped by some political science students of a local government college. They are annoyed that you keep on saying that political science is not a science. They blindfold you, put you at the back of van and drive off. But they don't know that students here are much smarter than them. From the noise of engine, you can make out that van is travelling at what speed. You mentally count off seconds and the turns van take. You know that the van travels in following manner. Take east as +ve x-axis and North as +ve y-axis. I. 36 km/hr for 10 sec. in east direction. II. 54 km/hr for 15 sec. after turning left. III. 45 km/hr for 16 sec. after turning right.
Q.4
Q.5
Q.6
What is the distance travelled by the van. (A) 525 m (B) 425 m What is the displacement of the van. (A) 525 m (B) 425 m
(C) 325 m
(D) 675 m [3]
(C) 375
(D) 675 m
If the van would have travelled with a constant speed, what would have that been so that it covers that [3] distance in same total time ? (A)
Q.7
[3]
425 41
m / s
525
(B)
m / s
41
(C)
325 41
m / s
On the basis of below diagram, mark correct option(s) :
(D)
625 41
m / s [4]
!
b
b a +
! !
!
R
=
a
(A) If a > b then ! < -
(B) If a < b then ! > -
(C) If a = b then ! = -
(D) If a * b then ! = -
!
!
PAGE # 3
Q.8
Considering Force (F), Velocity (V) and Energy (E) as fundamental quantities, match the correct [6] dimensions of following quantities. Column-I
(A) (B)
Mass Light year
(C)
Frequency
(D)
Pressure
Column-II
( 1 % & # ' T $
(P) (Q)
[F 1 V° E1] [F 1 V1 E 1]
(R)
[F3 V° E 2]
(S)
[F° V 2 E1]
–
–
–
–
Q.9
A sail boat sails 2km due East, 5km 37o South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is 6km due East, determine the third displacement. [5]
Q.10
Two horizontal forces of magnitudes 10 N & P N act on a particle. The force of magnitude 10 N acts due west & the force of magnitude P N acts on a bearing of 30° east of north as shown in figure. The resultant of these two force acts due [5] north. Find the magnitude of this resultant.
Q.11
When two vectors of magnitudes P and Q are inclined at an angle - the magnitude of their resultant 2P. When the inclination is changed to 180 – - the magnitude of the resultant is halved. Find the ratio of P to Q. [5]
PAGE # 4
PHYSICS
Daily Practice Problems Target IIT ENTRANCE 2014 Class:XI
Q.1
Discussion: 16-17/05/2012
M.M.: 37
DPP. NO.-6 [3]
The horizontal component of a force of 10 N inclined at 30° to vertical is : (B) 5 3 N
(A) 3 N
Q.2
Time: 40 Min.
(C) 5 N
(D)
10 3
N
A vector A is directed along 30 0 west of north direction and another vector B along 150 south of !
!
[3]
east. Their resultant cannot be in _____________ direction. (A) North (B) East (C) North-East !
(D) South
!
!
Q.3
Two vector a and b add to give a resultant c * a + b . In which of these cases angle between a and b [3] is maximum : (a, b, c represent the magnitudes of respective vectors) (A) c = a + b (B) c2 = a2 + b2 (C) c = a – b (D) Can not be determined
Q.4
A person pushes a box kept on a horizontal surface with force of 100 N. In unit vector notation force F [3] can be expressed as :
!
!
!
!
!
y 45
°
x
F
(A) 100 ( i + j) ˆ
ˆ
(B) 100 ( i , j) ˆ
(C) 50 2 ( i , j)
ˆ
ˆ
ˆ
(D) 50 2 ( i + j) ˆ
ˆ
Q.5
The following set represents magnitudes of three vectors. Which set of vectors can never give a zero [3] vector on addition ? (A) 3, 4, 5 (B) 2, 1, 3 (C) 12, 10, 23 (D) 13, 5, 12
Q.6
A car is moving in east direction. It takes a right turn and moves along south direction without change in [3] its speed. What is the direction of average acceleration of the car. (A) North east (B) South east (C) North west (D) South west
Q.7
A cable stretched between the fixed supports A and B is under a tension T of 1000 N. Express the !
tension as a vector using the unit vectors ˆi and j , first, as a force TA acting on A and second, as a force ˆ
!
[4]
TB acting on B. 3m
A
4m y x
B
(A) TA * (600ˆi , 800 jˆ) N
(B) TB * (,600ˆi + 800 jˆ) N
(C) TA * (800ˆi , 600 jˆ) N
(D) TB * (,800ˆi + 600 jˆ) N
!
!
!
!
PAGE # 5
Q.8
The displacement of air particle in a flute is given by x = a sin (.t) cos (kx) where t is time in second and . is a quantity which depends on the length of the flute (L), gas constant (R), temperature of air (T) and mass per unit mole of the air (/). Find an expression for . in terms of all these quantities [5] [Use PV = nRT]
Q.9
In the diagram below, the vectors u and v are at right angles to each other. The !
!
length of v is d. The horizontal and vertical components of u are a and b respectively. !
!
Find the vertical component of v in terms of a, b and d. !
Q.10
[5] A problem in I. E. Irodov's book is given as below: " A particle of mass m is located in a region where its potential energy [U(x)] depends on the
position x as Potential Energy [U(x)] =
(i) (ii)
[5]
a
,
b
x 2 x
here a & b are positive constants ..."
Write dimensional formula of a & b If the time period of oscillation which is calculated from above formula is stated by a student as T = 40a
ma b
2
, check whether his answer is dimensionally correct.
PAGE # 6
