1

JAMIA MILLIA ISLAMIA

875.176.862.4648.5458

Computer engineering
JEE ADVANCED - PHYSICS

Time Allowed: 3 minutes Maximum Marks : 390

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Section A 6) Which of the following have the same dimensions? [3]

1) The unit of surface tension may be expressed as: [3] a) Pressure and density
a) Joule metre - 2 b) Newton metre - 2 b) Stress and strain
c) Joule metre d) Newton metre c) Impulse and momentum
d) Gravitational potential and energy
2) In a screw gauge, the zero of the main scale coincides
with the fifth division of circular scale in figure (i). The
7) If force (F), length (L) and time (T) are taken as the
circular division of the screw gauge is 50. It moves 0.5
fundamental quantities. Then what will be the dimension
mm on the main scale in one rotation. The diameter of
of density: [3]
the ball in figure (ii) is
a) [FL - 5 T2 ] b) [FL - 3 T3 ]
c) [FL - 4
T]2
d) [FL - 3 T2 ]
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8) The density of a solid ball is to be determined in an

experiment. The diameter of the ball is measured with
a screw gauge, whose pitch is 0.5 mm and there are
50 divisions on the circular scale. The reading on the
main scale is 2.5 mm and that on the circular scale is 20
[3] divisions. If the measured mass of the ball has a relative
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a) 1.20 mm b) 1.25 mm error of 2%, the relative percentage error in the density
c) 2.20 mm d) 2.25 mm is [3]
( )
3) The dimension of 12 ε0 E 2 (ε0 : permittivity of free a) 3.1% b) 0.9%
space, E : electric field) [3] c) 4.2% d) 2.4%
a) MLT - 1 b) ML - 1 T - 2 9) Young’s modulus of elasticity Y is expressed in terms
c) ML T 2 - 1
d) ML2 T - 2 of three derived quantities, namely, the gravitational con-
4) If the units of mass, length and time are doubled, unit stant G, Planck’s constant h and the speed of light c,
of angular momentum will be: [3] asY = cα hβ Gγ . Which of the following is the correct
option? [3]
a) Quadrupled
b) 8 times the original value a) α = −7, β = 1, γ = −2
c) Tripled b) α = −7, β = −1, γ = −2
d) Doubled c) α = 7, β = −1, γ = 2
( ) d) α = 7, β = −1, γ = −2
5) The dimension of 12 ε0 E 2 (ε0 : permittivity of free
space, E electric field) [3]
10) The circular scale of a screw gauge has 50 divisions and
a) ML2 T - 1 b) ML2 T - 2
pitch of 0.5 mm. Find the diameter of sphere. Main
c) MLT - 1 d) ML - 1 T - 2
scale reading is 2.
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a) 0.05 mm b) 0.1 mm
c) 0.02 mm d) 0.2 mm
15) Which of the following set have different dimensions?
[3]

a) Pressure, Young’s modulus, Stress

[3] b) Dipole moment, Electric flux, Electric field
a) 2.20 mm b) 1.25 mm c) Heat, Work done, Energy
c) 2.25 mm d) 1.2 mm d) EMF, Potential difference, Electric potential
11) Area of the cross - section of a wire is measured using 16) A physical quantit y = (cda4 b)1/3 has four observables a, b,
4 2

a screw gauge. The pitch of the main scale is 0.5 mm. c and d. The percentage error in a, b, c, and d are 2%,
The circular scale has 100 divisions and for one full 3%, 4% and 5% respectively. The error in y will be: [3]
rotation of the circular scale, the main scale shifts by two a) 11% b) 12%
divisions. The measured readings are listed below. c) 6 % d) 22%
Measurement Main scale Circular
condition reading scale reading 17) Which of the following sets have different dimensions?
Two arms of 0 division 4 divisions [3]
gauge a) Heat, Work done, Energy
touching b) Dipole moment, Electric flux, Electric field
each other c) Emf, Potential difference, Electric potential
without wire d) Pressure, Young’s modulus, Stress
Attempt - 1: 4 divisions 20 divisions
With wire 18) A student performs an experiment to determine the
Attempt - 2: 4 divisions 16 divisions Young’s modulus of a wire, exactly 2 m long, by Searle’s
With wire method. In a particular reading, the student measures the
extension in the length of the wire to be 0.8 mm with
What are the diameter and cross - sectional area of the an uncertainty of± 0.05 mm at a load of exactly 1.0 kg.
wire measured using the screw gauge? [3] The student also measures the diameter of the wire to be
0.4 mm with an uncertainty of ± 0.01 mm. Take g =
a) 2.22± 0.02 mm, π (1.23 ± 0.02)mm2 9.8 m /s2 (exact). The Young’s modulus obtained from
b) 2.22± 0.01 mm, π (1.23 ± 0.01)mm2 the reading is close to [3]
c) 2.14± 0.01 mm, (1.14 ± 0.01)mm2
a) (2.0± 0.2) × 1011 N/m2
π
d) 2.14± 0.02 mm, (1.14 ± 0.02)mm2
b) (2.0± 0.1) × 1011 N/m2
π
c) (2.0± 0.05) × 1011 N/m2
12) Dimensions of electrical resistance is: [3] d) (2.0± 0.3) 1011 N/m2
a) [ML - 1 t3 A2 ] b) [ML3 T - 3 A - 2 ]
c) [ML T2 - 3
A ] - 1
d) [ML2 T - 3 A - 2 ] 19) A cube has a side of length 1.2× 10 - 2 m. Calculate
its volume. [3]
13) Students I, II and III perform an experiment for mea- a) 1.732× 10 - 6 m3 b) 1.73× 10 - 6 m3
suring the acceleration due to gravity (g) using a simple c) 1.7× 10 - 6
m3
d) 1.70× 10 - 6 m3
pendulum. They use different lengths of the pendulum
20) A ( student )performs an experiment for determination
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and/or record time for a different number of oscillations.

The observations are shown in the table. Least count for ofg = 4π . The error in length l is ∆l and in time
2
ℓ
T2
length = 0.1 cm, Least count for time = 0.1s T is ∆T and n is number of times the reading is taken.
Student Length Number Total Time The measurement of g is most accurate for [3]
of the of os- time period
pendu- cilla- for (n) (s) a) ∆l = 1 mm, ∆T = 0.1 sec, n = 50
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lum tions(n) oscil- b) ∆l = 5 mm, ∆T = 0.2 sec, n = 10

lations c) ∆l = 5 mm, ∆T = 0.1 sec, n = 10
(s) d) ∆l = 5 mm, ∆T = 0.2 sec, n = 20
I 64.0 8 128.0 16.0 21) The smallest division on the main scale of a Vernier
calipers is 0.1 cm. Ten divisions of the Vernier scale
II 64.0 4 64.0 16.0 correspond to nine divisions of the main scale. The figure
below on the left shows the reading of this calipers with
III 20.0 4 36.0 9.0 no gap between its two jaws. The figure on the right
shows the reading with a solid sphere held between the
jaws. The correct diameter of the sphere is
If El , EII )and EIII are the percentage errors in g, i.e.
(
g × 100
∆g
for students I, II and III, respectively. [3]
a) E1 = 0 b) El = EII
c) EII is maximum d) EI is minimum
14) A vernier calipers has 1 mm marks on the main scale. It
[3]
has 20 equal divisions on the vernier scale which match
a) 3.11 cm b) 3.07 cm
with 16 main scale divisions. For this vernier calipers,
c) 3.15 cm d) 3.17 cm
the least count is [3]
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22) A quantity X is given byε0 L ∆V∆t where ϵ0 is the permit- time, the horizontal component of its velocity is v. A
tivity of the free space, L is a length, ∆V is a potential bead Q of the same mass as P is ejected from A at t = 0
difference and ∆t is a time interval. The dimensional along the horizontal string AB, with the speed v. Friction
formula for X is the same as that of [3] between the bead and the string may be neglected. Let
a) Voltage b) Current tP and tQ be the respective times taken by P and Q to
c) Charge d) Resistance reach the point B. Then
23) Which of the following product of e, h,µ , G (where µ
is the permeability) be taken so that the dimensions of
the product are same as that of the speed of light? [3]
a) H0 e2 G - 1 µ b) HGe - 2 µ0 [3]
c) H µ- 2 −1
G 0
d) H - 2 eG0 µ
( αz ) a) TP > tQ
24) Pressure depends on distance as,P = α β exp − kθ , where b) TP = tQ
α, β are constants, z is distance, k is Boltzmann’s constant c) TP < tQ
and θ is temperature. The dimension of β are [3] d) ttQ
P length of arc ACB
= length
a) M 0 L0 T 0 b) M 0 L2 T 0 of chord AB

c) M L T
−1 −1 −1
d) M −1 L1 T 2 32) A river is flowing from west to east at a speed of 5
25) In the determination of Young’s modulus (Y = )
4M Lg metres per minute. A man on the south bank of the
by using Searle’s method, a wire of length L = 2m and
πld2
river, capable of swimming at 10 metres per minute in
diameter d = 0.5 mm is used. For a load M = 2.5 kg, still water, wants to swim across the river in the shortest
an extension l = 0.25 mm in the length of the wire is time. He should swim in a direction: [3]
a) Due north b) 30o east of north
observed. Quantities d and l are measured using a screw
c) 60 east of north
o
d) 30o west of north
gauge and a micrometer, respectively. They have the
same pitch of 0.5 mm. The number of divisions on their 33) If the two vectorsA⃗ = 2î + 3ĵ + 4k̂ and B
⃗ = î + 2ĵ − nk̂
circular scale is 100. The contributions to the maximum are perpendicular, then the value of n is: [3]
probable error of the Y measurement is [3] a) 3 b) 2
c) 4 d) 1
a) Due to the errors in the measurements of d and l
are the same 34) A boat crosses a river of width 1 km along the shortest
b) Due to the error in the measurement of d is twice path in 15 minutes. If the speed of boat in still water is
that due to the error in the measurement of l 5 km/hr, then what is the speed of the river? [3]
c) Due to the error in the measurement of d is four a) 2 km/hr b) 1 km/hr
times that due to the error in the measurement of l c) 3 km/hr d) 5 km/hr
d) Due to the error in the measurement of l is twice 35) A bomb is dropped from an aeroplane when it is directly
that due to the error in the measurement of d above a target at a height of 1254.4 m. The aeroplane is
26) A wire of lengthℓ = 6 ± 0.06 cm and radius r = 0.5 going horizontally with a speed of 150 m/s. The distance
± 0.005 cm and mass m = 0.3 ± 0.003 gm. Maximum by which it will miss the target is: [3]
percentage error in density is [3] a) 1.2 km b) 2.8 km
a) 2 b) 4 c) 2.4 km d) 1.8 km
c) 6.8 d) 1 36) IfA
⃗=B ⃗ +C ⃗ and the values of A,⃗ B⃗ and C ⃗ are 13,
12 and 5 respectively, then the angle between A⃗ and C
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27) A boat which has a speed of 5 km/h in still water crosses

⃗
a river of width 1 km along the shortest possible path in will be: [3]
15 min. The velocity of the river water
√ in km/h is [3] a) Cos - 1 ( 135
)
a) 3 b) 41 b) Sin - 1
( 12 )
5
c) 1 d) 4 c) π2
28) A train is moving north with speed 20 ms - 1 . If it turns 12 )
d) Cos - 1 ( 13
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west with same speed, then the change in velocity will

37) A river is flowing from West to East at a speed of 5
be: [3] √
a) 20√2 ms - 1 N - W b) 40 ms - 1 N - E m/min. A man on the South Bank of the river, capable
of swimming at 10 m/min in still water, wants to swim
c) 20 2 ms S - W
- 1
d) 20 ms - 1 S - E
across the river in the shortest time. He should swim in
29) A ball falls from height h. After 1 second, another ball a direction [3]
falls freely from a point 20 m below the point from a) 30o East of North b) Due North
where the first ball falls. Both of them reach the ground c) 60o East of North d) 30o West of North
at the same time. What is the value of h? [3] → −
− → −
→
a) 41.2 m b) 21.2 m 38) There vectors P , Q and R are shown in the figure. Let
−
→
c) 31. 2 m d) 11.2 m S be any point on the vector R . The general relation
→ −
− → −
→
among vectors P , Q and S is
30) An object is projected at an angle of 45o with the hori-
zontal. The horizontal range and maximum height reached
will be in the ratio of: [3]
a) 1 : 4 b) 2 : 1
c) 1 : 2 d) 4 : 1
[3]
31) A particle P is sliding down a frictionless hemispherical
→ (
− )−
→ −
→
bowl. It passes the point A at t = 0. At this instant of a) S = 1 − b2 P + b Q
 4

−
→ −
→ −
→
b) S = (1 − b) P + b Q 47) The side of a cube is measured by vernier callipers (10
−
→ −
→ −
→ divisions of a vernier scale coincide with 9 divisions of
c) S = (1 − b) P + b2 Q
d)
−
→ −
→ −
→
S = (b − 1) P + b Q the main scale, where 1 division of the main scale is 1
mm). The main scale reads 10 mm and the first division
39) During a projectile motion, if the maximum height equals of the vernier scale coincides with the main scale. The
to the horizontal range, then the angle of projection with mass of the cube is 2.736 g. Find the density of the
the horizontal is: [3] cube in the appropriate significant figures. [4]
a) tan−1 (1) b) tan−1 (3) 48) An optical bench has a 1.5 m long scale having four
c) tan (4)
−1
d) tan−1 (2) equal divisions in each cm. While measuring the focal
40) The angle between the vectors(î + ĵ) and (ĵ + k̂) is: [3] length of a convex lens, the lens is kept at the 75 cm
a) 30° b) 45° mark of the scale and the object pin is kept at the 45 cm
c) 60o d) 90° mark. The image of the object pin on the other side of
the lens overlaps with the image pin that is kept at the
41) A boat which has a speed of 5 km per hour in still water 135 cm mark. In this experiment, the percentage error in
crosses a river of width 1 km along the shortest possible the measurement of the focal length of the lens is .
path in fifteen minutes. The velocity of the river water [4]
(in km√ per hour) is: [3] 49) To find the distance d over which a signal can be seen
a) 41 b) 2 clearly in foggy conditions, a railways - engineer uses
c) 1 d) 3 dimensions and assumes that the distance depends on the
√
42) If|A
⃗ × B|
⃗ = 3(A ⃗ , then the value of |A
⃗ · B) ⃗ is:
⃗ + B| mass densityρ of the fog, intensity (power/area) S of the
[3] light from the signal and its frequency f. The engineer
( ) 12 finds that d is proportional to S1/n . The value of n is [4]
a) A2 + B 2 + AB
√ 50) Two vectorsA ⃗ and B ⃗ are defined as A ⃗ = aî and B ⃗
= a(cos ω t î + sin ω t ĵ ), where √ a is a constant
3
b) A + B
( )1 and ω = π6 rad s - 1 . If |A ⃗ + B|
⃗ = 3|A ⃗ at time
⃗ − B|
c) A2 + B 2 + AB 2
( √ )1 t = τ for the first time, the value of τ , in seconds, is
d) A2 + B 2 + 3AB 2 . [4]
43) Match List I with List II : 51) A projectile is thrown from a point O on the ground at
List I List II an angle 45o from the vertical and with a speed 5 m/s.
(a) Boltzmann (i) [ML2 T - 1 ] The projectile at the highest point of its trajectory splits
constant into two equal parts. One part falls vertically down to
(b) Coefficient of (ii) [ML - 1
T - 1
] the ground, 0.5 s after the splitting. The other part, t
viscosity seconds after the splitting, falls to the ground at a dis-
(c) Planck constant (iii) [MLT - 3
K - 1
] tance x meters from the point O. The acceleration due to
gravity g = 10 m/s2 .
(d) Thermal (iv) The value of x is . [4]
conductivity [ML2 T - 2
K - 1
] 52) A train is moving along a straight line with a constant
acceleration a. A boy standing in the train throws a ball
forward with a speed of 10 m/s, at an angle of 60° to
[3] the horizontal. The boy has to move forward by 1.15
m inside the train to catch the ball back at the initial
a) (a) - (iii), (b) - (ii), (c) - (i), (d) - (iv)
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height. The acceleration of the train, in m/s2 , is. [4]

b) (a) - (iv), (b) - (ii), (c) - (i), (d) - (iii)
53) A projectile is thrown from a point O on the ground√at
c) (a) - (iii), (b) - (i), (c) - (ii), (d) - (iv)
an angle 45o from the vertical and with a speed 5 2
d) (a) - (iv), (b) - (i), (c) - (ii), (d) - (iii)
m/s. The projectile at the highest point of its trajectory
Section B splits into two equal parts. One part falls vertically down
to the ground, 0.5 s after the splitting. The other part,
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44) In an experiment for determination of the focal length of t seconds after the splitting, falls to the ground at a
a thin convex lens, the distance of the object from the distance x meters from the point O. The acceleration due
lens is 10± 0.1 cm and the distance of its real image to gravity g = 10 m/s2 .
from the lens is 20 ± 0.2 cm. The error in the determi- The value of t is . [4]
nation of focal length of the lens is n%. The value of n 54) A projectile is fired from horizontal ground with speed
is . [4] v and projection angleθ . When the acceleration due
45) In a particular system of units, a physical quantity can to gravity is g, the range of the projectile is d. If at
be expressed in terms of the electric charge e, electron the highest point in its trajectory, the projectile enters a
mass me , Planck’s constant h, and Coulomb’s constant different region where the effective acceleration due to
k = 4πϵ1
, where ϵ0 is the permittivity of vacuum. In gravity is g’ = 0.81
g
, then the new range is d’ = nd.
terms of these physical constants, the dimension of the
0

The value of n is . [4]

magnetic field is [B] = [e]α [me ] [h]γ [k]δ . The value of 55) Using the expression 2d sinθ = λ , one calculates the
β

α + β + γ + δ is . [4] values of d by measuring the corresponding angles θ in

46) A screw gauge having 100 equal divisions and a pitch of the range 0 to 90o . The wavelength λ is exactly known
length 1 mm is used to measure the diameter of a wire and the error in θ is constant for all values of θ . As
of length 5.6 cm. The main scale reading is 1 mm and θ increases from 0o . [4]
the 47th circular division coincides with the main scale.
Find the curved surface area of the wire in cm2 to an a) The absolute error in d remains constant
appropriate significant figure. (use π = 22 7 ) [4] b) The fractional error in d remains constant
 5

c) The fractional error in d decreases a) If the least count of the linear scale of the screw
d) The absolute error in d increases gauge is twice the least count of the Vernier cal-
lipers, the least count of the screw gauge is 0.01
56) Planck’s constant h, speed of light c and gravitational
mm
constant G are used to form a unit of length L and a
b) If the pitch of the screw gauge is twice the least
unit of mass M. Then the correct option(s)
√ is(are) [4]
√ count of the Vernier callipers, the least count of the
a) M ∝√ c b) M ∝√ G screw gauge is 0.01 mm
c) L ∝ h d) L ∝ G c) If the pitch of the screw gauge is twice the least
57) In an experiment to determine the acceleration due to count of the Vernier callipers, the least count of the
gravity g, the formula used screw gauge is 0.005 mm
√ for the time period of a
d) If the least count of the linear scale of the screw
periodic motion is T =2π 7(R−r) . The values of R
5g gauge is twice the least count of the Vernier cal-
and r are V 5g measured to be (60 ± 1) mm and (10
lipers, the least count of the screw gauge is 0.005
± 1) mm, respectively. In five successive measurements,
mm
the time period is found to be 0.52s, 0.56s, 0.57s, 0.54s
and 0.59s. The least Count of the watch used for the 63) The dimensions of the quantities in one (or more) of the
measurement of time period is 0.01 s. following pairs are the same. Identify the pair (s) [4]
Which of the following statement(s) is (are) true? [4] a) Energy and Young’s modulus
a) The error in the determined value of g is 11% b) Light year and Wavelength
b) The error in the measurement of r is 10% c) Angular momentum and Work
c) The error in the measurement of T is 3.75% d) Torque and Work
d) The error in the measurement of T is 2% 64) A physical quantityS ⃗ is defined as S
⃗ = (E ⃗ × B)/µ
⃗ 0 ,

58) The SI unit of inductance, the henry can be written as where E ⃗ is electric field, B
⃗ is magnetic field and µ0 is
[4] the permeability of free space. The dimensions of S ⃗ are
a) Ohm - second b) Volt - sec/amp the same as the dimensions of which of the following
c) Weber/ampere d) Joule/(ampere)2 quantities? [4]
Energy
59) Sometimes it is convenient to construct a system of units a) Volume
Energy
so that all quantities can be expressed in terms of only b) Charge × Current
one physical quantity. In one such system, dimensions of c) Power
Area
different quantities are given in terms of a quantity A as d) Force
Length × Time
follows: [ ]
[position]= [X α ] ; [speed]= X β ; [acceleration]= [Xp ]; 65) In terms of potential difference V, electric current I,
[linear momentum]= [Xq ]; [force]= [Xr ]. Then [4] permittivityε0 , permeability µ0 and speed of light c, the
a) P + q - r =β b) P + q + r =β dimensionally correct equation(s) is(are) [4]
c) α + p = 2β d) P - q + r =α a) ε0 I = µ0 V
60) Let us consider a system of units in which mass and b) I = ε0 cV
angular momentum are dimensionless. If length has di- c) µ0 I 2 = ε0 V 2
mensions of L, which of the following statement(s) is/are d) µ0 cI = ε0 V
correct? [4] 66) Let [ε0 ]denote the dimensional formula of the permittiv-
ity of the vacuum, and [µ0 ]that of the permeability of
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a) The dimension of force is L- 2

the vacuum. If M = mass, L = length, T = time and I
b) The dimension of linear momentum is L - 1
= electric current, [4]
c) The dimension of energy is L - 2
d) The dimension of power is L - 5 a) [µ0 ] = M LT −2 I −2
b) [ε0 ] = M −1 L−3 T 2 I
61) A student uses a simple pendulum of exactly 1 m length c) [µ0 ] = M L2 T −1 I
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to determine g, the acceleration due to gravity. He uses d) [ε0 ] = M −1 L−3 T 4 I 2

a stop watch with the least count of 1 sec for this and
records 40 seconds for 20 oscillations. For this obser- 67) The pairs of physical quantities that have the same di-
vation, which of the following statement(s) is (are) true? mensions is (are): [4]
[4] a) Curie and frequency of a light wave
a) Error∆ T in measuring 7, the time period, is 1 b) Reynolds number and coefficient of friction
second c) Latent heat and gravitational potential
b) Percentage error in the determination of g is 2.5% d) Planck’s constant and torque
c) Percentage error in the determination of g is 5% 68) A length - scale (l) depends on the permittivity (ε ) of a
d) Error∆ T in measuring 7, the time period, is 0.05 dielectric material. Boltzmann constant (kB ), the absolute
seconds temperature (T), the number per unit volume (n) of certain
charged particles, and the charge (q) carried by each of
62) Consider a Vernier callipers in which each 1 cm on the
the particles. Which of the following expression(s) for l
main scale is divided into 8 equal divisions and a screw
is(are) dimensionally correct? [4]
gauge with 100 divisions on its circular scale. In the √(
Vernier callipers, 5 divisions of the Vernier scale coin- )
εkB T
a) l =
cide with 4 divisions on the main scale and in the screw nq 2
√( )
gauge, one complete rotation of the circular scale moves nq2
it by two divisions on the linear scale. Then: [4] b) l = εkB T
 6
√( )
q2 c) |α| cannot exceed 2 at any point in its path.
c) l =
√(
εn1/3 kB T d) α must change sign during the motion, but no other
) assertion can be made with the information given.
q2
d) l = εn2/3 k BT

Section C
69) A particle of mass m moves on the x - axis as follows
: it starts from rest at t = 0 from the point x = 0, 70) State whether the given statement is True or False: [8]
and comes to rest at t = 1 at the point x = 1. NO (a) Two identical trains are moving on rails along the
other information is available about its motion at inter- equator on the earth in opposite directions with the
mediate times (0 < t < 1). If a denotes the instantaneous same speed. They will exert the same pressure on
acceleration of the particle, then: [4] the rails. [4]
a) α cannot remain positive for all t in the interval 0 (b) A projectile fired from the ground follows a parabolic
≤ t ≤ 1. path. The speed of the projectile is minimum at the
b) |α| must be ≥ 4 at some point or points in its path. top of its path. [4]
RO
IS