(speed of light in vacuum), h (Planck's constant) and G

74 Pages·2017·0.79 MB·English

by  Asus S400

Test40TestID218Key 1
PHYSICS
Consider a new system of units in which c (speed of light in vacuum), h
1.
(Planck’s constant) and G (gravitational constant) are taken as fundamental
units.
Which of the following would correctly represent mass in this new system?
hc
G
A.
Gc
h
B.
hG
c
C.
hGc
D.
DetailedAnswer::
a)
[m] hx.cy.Gz
GMm
Using E  h, E  mc2 and F 
r2
y
Ex  E12 F.r2z
[m]   .   . 
 m   Mm
 
y
ML2T2xML2T22MLT2.L2z
M1LoTo       
 T1   M   M2 
y
[ML2T1]x [L2T2]2.[M1.L3.T2]z
M1L°T° = Mx-zL2x-y+3zT-x-y-2z
Equating the powers of x, y, z we get
x - z = 1 …………….(1)
2x + y + 3z = 0 …………..(2)
-x - y - 2z = 0 ……………..(3)
Substituting z = x - 1 from (1) in (2) and (3),
we get
2x+y+3(x-1) = 0 ………….(2’)
-x-y-2(x-1)=0 ……………(3’)
PRESCIENTACADEMY
Test40TestID218Key 2
 5x+y=3 ……………...(2”)
and -3x - y = -2 ………...(3”)
Adding (2”) and (3”), we get
1 1 1
2x = 1 or x =  z  x1 1 
2 2 2
5 1
Further, y = 3 - 5x = 3- 
2 2
1 1 1 1 1 1
 x  ,y  ,z    m  h2.c2.G 2
2 2 2
h.c
or m  .
G
Answer::A
[PrescientAcademyQRefNo: 45-12] [1.PHYSICSANDMEASUREMENT]
Abullet fired at an angle of 30o with the horizontal hits the ground 3 km
2.
away. By adjusting its angle of projection, what is the farthest distance can
one hope to hit
3.46 km
A.
3.82 km
B.
4.12 km
C.
4.46 km
D.
DetailedAnswer::
u2.sin2
3km
g
u2 3
Here 300,so 
g sin600km
u2 3x2 6
Bur R    km  2 3 3.46km.
max g 3 3
Answer::A
[PrescientAcademyQRefNo: 46-33] [2.KINEMATICS]
. If AB BA, then the angle between A and B is
3.
PRESCIENTACADEMY
Test40TestID218Key 3

A.
/3
B.
/2
C.
/4
D.
DetailedAnswer::
   
AxB  Bx A
 
or ABsinn  ABsin()n
or sin sin or 2sin 0
or  0,,2..... .
Answer::A
[PrescientAcademyQRefNo: 46-5] [2.KINEMATICS]
Aprojectile can have the same range for two angles of projection. If h and
4. 1
h are maximum heights when the range in the two cases is R, then the
2
relation between R, h and h is
1 2
R  4 h h
A. 1 2
R  2 h h
B. 1 2
R  h h
C. 1 2
none of these
D.
DetailedAnswer::
u2sin2
h 
1 2g
u2sin2(900 ) u2sin2
h  ,R 
2 2g g
Range R is same for angles  and (900 - )
u2sin2 u2sin2(90)
h h  x
1 2 2g 2g
PRESCIENTACADEMY
Test40TestID218Key 4
u4(sin2)xsin2(90)

4g2
[sin(90)  cos]
u4(sin2)xcos2 u2(2sincos)2
 
4g2 4g2x4
u4(sin2)2 R2
 
16g2 16
or R2 16h h or R  4 h h
1 2 1 2
Answer::A
[PrescientAcademyQRefNo: 46-9] [2.KINEMATICS]
The coefficient of friction between two surfaces is 0.2. The angle of
5.
friction is
sin-1 (0.2)
A.
cos-1 (0.2)
B.
tan-1 (0. 1)
C.
cot-1 (5)
D.
DetailedAnswer::
Angle of sliding or repose is the angle that an inclined plane makes with the
horizontal when a body place on it just starts sliding down.
F N
max
N  mgcos
mgsin f
max
 mgsinN mgcos
or  tan
1
Here,0.2  tan or cot 5
0.2
 cot1(5).
PRESCIENTACADEMY
Test40TestID218Key 5
Answer::D
[PrescientAcademyQRefNo: 47-8] [3.LAWSOFMOTION]
In diagram, find out the weight registered by the weighing machine.
6.
(m +m )a
A. 1 2
(m + 2m )g + (m + m )a
B. 1 2 1 2
(m +m )g+(m -m )a
C. 1 2 1 2
(m -m )a +(m +m )g
D. 1 2 1 2
DetailedAnswer::
The free body diagram of the given problem is:
Here the normal force acting on the weighing machine is,
N  N  N
…(1)
1 2
m
Constraint in the given problem is, what ever may be the acceleration of
1
should have it upwards. {This is obvious because the plank holding masses
is considered to the rigid}.
m m
Force equations: From individual F.B.D. of mass 1and 2, we have
m : N m g  m a which implies
Mass 1 1 1 1
N  m (g a)
1 1 ..(2)
m g  N  m a which implies
Mass
2 2 2
N  m (g a)
…(3)
2 2
Equation (2) added to (3) and compared with equation (1) gives,
N  (m m )g (m m )a
1 2 1 2
This is the weight registered by the weighing machine.
Answer::C
[PrescientAcademyQRefNo: 47-16] [3.LAWSOFMOTION]
PRESCIENTACADEMY
Test40TestID218Key 6

Abody of density and volume V is lifted through height h in a liquid
7.
of density  (<). The increase in potential energy of the body is
V ( - ) gh
A.

V gh
B.
V  gh
C.
zero
D.
DetailedAnswer::
Answer::A
[PrescientAcademyQRefNo: 48-15] [4.WORK,ENERGYANDPOWER]
Anucleus ruptures into two nuclear parts which have their velocity ratio
8.
equal to 2 : 1. The ratio of their respective nuclear sizes (nuclear radii) is
1 : 2
A.
1: 2
B.
1 : 21/3
C.
1 : 8
D.
DetailedAnswer::
Answer::C
[PrescientAcademyQRefNo: 48-13] [4.WORK,ENERGYANDPOWER]
9.Four identical planks each oflengths ‘L’are arranged one abovetheother over atable
as shown. Each projects adistance‘a’beyond the edge oftheonethat is belowit.What is
themaximumpossiblevalue of‘a’forthesystem tobein equilibrium withouttripping
forward?
A.L/5
PRESCIENTACADEMY
Test40TestID218Key 7
B.L/4
C.L/3
D.L
DetailedAnswer::
CM of bricks, above each brick must not be
m x
beyond its edge. X  i i ; x  L
cm m cm
i
L L L
x  a ,x  2a  ,x 3a 
1 2 2 2 3 2
Answer::B
[PrescientAcademyQRefNo: 49-11] [5.ROTATIONALMOTION]
10. Mass of a ring is non-uniformly distributed around its geometric centre. If R is radius
ofthering, then
a. centre of mass does not coincide withgeo-metric centre
b.Positioncentre ofmass from thegeometric centre willbe x(O<x<R)
c. centre of mass willbe nearerto thegreater mass distribution
d.centre ofmass may lieoutsidetheperiphery
A.onlya&barecorrect
B.onlyb&carecorrect
C.a,b&carecorrect
D.Allthecorrect
Answer::A
[PrescientAcademyQRefNo: 49-13] [5.ROTATIONALMOTION]
The question contains statement-1 (Assertion) and Statement-2 (Reason).
11.
It has four choices. You have to select the correct choice.
Assertion : A satellite moves round the earth in a circular orbit under the
action of gravity. A person in the satellite experience a zero gravity field in
the satellite.
Reason : The contact force by the surface on the person is zero.
if statement-1 is true but statement 2 is false.
A.
if statement-1 is false and statement-2 is true.
B.
PRESCIENTACADEMY
Test40TestID218Key 8
if both statement-1 and statement-2 are true and statement-2 is the correct
C.
explanation of statement-1.
if both statement-1 and statement-2 are true but statement-2 is not the
D.
correct explanation of statement-1.
DetailedAnswer::
(b) : The person experiences zero net force as the force of gravity is
balanced by the centrifugal force inside the satellite.
Answer::B
[PrescientAcademyQRefNo: 4A-12] [6.GRAVITATION]
12.Spherical balls of radius R are falling in a viscous fluid of viscosity nwith a velocity v.
Theretarding viscous force acting onthespherical ball is
A.directly proportional to Rbut inversely proportional tov
B.directly proportional to bothradius Rand velocity v
C.inversely proportional to bothradius R andvelocity v
D.inversely proportional to R but directly proportional tovelocity v
Answer::B
[PrescientAcademyQRefNo: 4B-2] [7.PROPERTIESOFSOLIDSANDLIQUIDS]
13.The freezer in arefrigerator islocated at thetop section so that
A.entire chamber oftherefrigerator iscooled quicklydue to convection
B.motorisnot heated
C.heat gained from theenvironment ishigh
D.heat gained from theenvironment islow
Answer::A
[PrescientAcademyQRefNo: 4C-7] [8.THERMODYNAMICS]
14.Ametal ball suspended from thehookofa spring balance is kept immersed in a liquid
otherthan water.On increasing thetemperature ofthis liquid, thereading inthespring
balance
A.increases
PRESCIENTACADEMY
Test40TestID218Key 9
B.decreases
C.remains same
D.may increases ordecreases
DetailedAnswer::
Answer::A
[PrescientAcademyQRefNo: 4D-3] [9.KINETICTHEORYOFGASES]
15.The normal boilingpoint ofliquidhydrogen is -253ºC.Whatis thecorresponding
temperatureonabsolutescale
A.22K
B.20K
C.274K
D.-20 K
DetailedAnswer::
C = K- 273
Answer::B
[PrescientAcademyQRefNo: 4D-49] [9.KINETICTHEORYOFGASES]
16.Coefficient oflinear expansionof acrystal in3mutually perpendicular directions are
8.5×10-6/ºC,10.5× 10-6/ºC,11× 10-6/ºC.If mass ofcrystal is25gm, its volumeat 60ºcis
(given density at 0ºC is 5g/cc)
A.5.009c.c.
B.4.991c.c.
C.5.9c.c.
D.5.999c.c.
DetailedAnswer::
  
x y z
m
V  ; V V [l  t]
o d 1 o
o
Answer::A
PRESCIENTACADEMY
Test40TestID218Key 10
[PrescientAcademyQRefNo: 4D-29] [9.KINETICTHEORYOFGASES]
17.Athree looppattern is observed in Melde’s experimentperformed inparallel position.
When theotherconditions are same, theexperiment is performed intransverse position,
theno.ofloops formed is
A.3
B.6
C.4
D.2
Answer::B
[PrescientAcademyQRefNo: 4E-29] [10.OSCILLATIONSANDWAVES]
18.In a long cylindrical tube, the waterlevel is adjusted and aircolumn above it is made
tovibrate inunison witha vibrating tuningfork kept at theopenend. Maximum soundis
heard whenair column lengths are equal to
A.λ/2,λ,3λ/2
B.λ/2,3λ/2, 5λ/2
C.λ/4,3λ/4, 5λ/4
D.λ/4,λ/4, 3λ/4
Answer::C
[PrescientAcademyQRefNo: 4E-35] [10.OSCILLATIONSANDWAVES]
19.Which ofthefollowing statements is wrong ?
A.Changes in air temperature have noeffect onthespeed of sound
B.Changes in air pressure have noeffect onthe speed ofsound
C.Thespeed ofsound in water ishigher than in air
D.Thespeed oflight in water is lowerthan inair
Answer::A
[PrescientAcademyQRefNo: 4E-28] [10.OSCILLATIONSANDWAVES]
20.Energy stored / unitvolumeinan electric field ofstrength E V/m ina medium of
dielectric constant K(in J/m3is)
PRESCIENTACADEMY