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# Units and Measurements Assignment Class 11 Notes | EduRev

## Class 11 : Units and Measurements Assignment Class 11 Notes | EduRev

``` Page 1

PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
XI ASSIGNMENT-1  : DIMENSION ANALYSIS & ERRORS
1. The velocity v of particle depends upon t according to the equation .
()
c
u a bt
dt
? ? ?
?
write the dimensions of a, b, c and d.
[Ans.
12
[ ],[ ],[ ],[ ]] LT LT L T
??

2. Write the dimension of ab is the relations
2
()
,
bx
E
at
?
?
where E is the energy, x is the
distance and t is the time.
[Ans.
12
[] M LT
?
]
3. Write the dimensions of (a/b) in the relation
2
()
,
at
p
bx
?
?
where P is the pressure, x is
the distance and t is the time.
[Ans.
2
[] MT
?
]
4. An apprentice engineer found that volume V of water which passes any point of
canal during time t is connected with the cross-section a of the canal and the velocity v
of water by the relation, V=kavt. Verify the correctness of the relation.
[Ans. Incorrect]
5. The height h to which a liquid of surface tent ion T and density p rises in a capillary of
radius r is given by the relation
2
2 cos T
h
rg
?
?
?
where
?
is the angle of contact and g is the
acceleration due to gravity. Verify the correctness of this statement.
[Ans. incorrect]
6. check the dimensional consistency of the formula,
1 B
u
p ?
?
,where v is the velocity of
the longitudinal waves, B is the bulk modulus and p is the density of the medium,
?
is
the wavelength of the waves.
[Ans. incorrect]
7. Check the correctness of the relation,
3
4
g
p
Rg ?
?
, where the letters have their usual
meaning.
[Ans. correct]
Page 2

PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
XI ASSIGNMENT-1  : DIMENSION ANALYSIS & ERRORS
1. The velocity v of particle depends upon t according to the equation .
()
c
u a bt
dt
? ? ?
?
write the dimensions of a, b, c and d.
[Ans.
12
[ ],[ ],[ ],[ ]] LT LT L T
??

2. Write the dimension of ab is the relations
2
()
,
bx
E
at
?
?
where E is the energy, x is the
distance and t is the time.
[Ans.
12
[] M LT
?
]
3. Write the dimensions of (a/b) in the relation
2
()
,
at
p
bx
?
?
where P is the pressure, x is
the distance and t is the time.
[Ans.
2
[] MT
?
]
4. An apprentice engineer found that volume V of water which passes any point of
canal during time t is connected with the cross-section a of the canal and the velocity v
of water by the relation, V=kavt. Verify the correctness of the relation.
[Ans. Incorrect]
5. The height h to which a liquid of surface tent ion T and density p rises in a capillary of
radius r is given by the relation
2
2 cos T
h
rg
?
?
?
where
?
is the angle of contact and g is the
acceleration due to gravity. Verify the correctness of this statement.
[Ans. incorrect]
6. check the dimensional consistency of the formula,
1 B
u
p ?
?
,where v is the velocity of
the longitudinal waves, B is the bulk modulus and p is the density of the medium,
?
is
the wavelength of the waves.
[Ans. incorrect]
7. Check the correctness of the relation,
3
4
g
p
Rg ?
?
, where the letters have their usual
meaning.
[Ans. correct]
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
8. The orbital velocity v of a satellite may depend on its mass m, the distance r form the
center of the earth and the acceleration due to gravity g. by the method of dimensional
analysis, obtain an expression of v.
[ . ] Ansv rg ?

9. A U-tube of uniform cross-section contains mercury up to a height h in either limb.
The mercury in one limb is depressed a little and then released. Obtain an expression
for the time period of oscillation.
[ . 2 ]
h
AnsT
g
? ?

10. Given the value of G in cgs system as 6.67X10
-8
dyne cm
2
/g
2
, find the value in mks
system in
22
/. Nm kg

11
[ .6.67 10 ] Ans
?
?

11. By the method of dimensions, show that energy per unit volume is dimensionally
equal to the pressure.
12. Express
46
3.0 10 1.7 10
??
? ? ?
with proper signification figures.
4
[ .3.0 10 ] Ans
?
?

13. The surface tent ion (T) is measured by capillary rise formula
2cos
rhpg
T
?
?
. The
quantities p.g and 0 are taken from the table of constants while height and diameter
are measured as h=(3.00+0.001)cm and D=(0.250+0.001)cm.find the percentage error
in T.
[Ans.07%)]
14. The period of oscillation of a simple pendulum is
2 1/ . Tg ? ?
The length
l
40cm and is known to 1 mm accuracy. The time of 50 oscillation is 80s measured with a
write watch of 1 s resolution. What is the error in the determination of g ?
[Ans.2.8%]
15. The radius of sphere is measured as (2.1+0.5)cm. calculate its surface area with
error limits.
2
[ .{(55.4 26.4) }] Ans cm ?

16. The voltage across  lamp is (6.0+0.1) volt and the current passing through it is
(4.0+0.2) ampere. Find the power consumed by the lamp.
Page 3

PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
XI ASSIGNMENT-1  : DIMENSION ANALYSIS & ERRORS
1. The velocity v of particle depends upon t according to the equation .
()
c
u a bt
dt
? ? ?
?
write the dimensions of a, b, c and d.
[Ans.
12
[ ],[ ],[ ],[ ]] LT LT L T
??

2. Write the dimension of ab is the relations
2
()
,
bx
E
at
?
?
where E is the energy, x is the
distance and t is the time.
[Ans.
12
[] M LT
?
]
3. Write the dimensions of (a/b) in the relation
2
()
,
at
p
bx
?
?
where P is the pressure, x is
the distance and t is the time.
[Ans.
2
[] MT
?
]
4. An apprentice engineer found that volume V of water which passes any point of
canal during time t is connected with the cross-section a of the canal and the velocity v
of water by the relation, V=kavt. Verify the correctness of the relation.
[Ans. Incorrect]
5. The height h to which a liquid of surface tent ion T and density p rises in a capillary of
radius r is given by the relation
2
2 cos T
h
rg
?
?
?
where
?
is the angle of contact and g is the
acceleration due to gravity. Verify the correctness of this statement.
[Ans. incorrect]
6. check the dimensional consistency of the formula,
1 B
u
p ?
?
,where v is the velocity of
the longitudinal waves, B is the bulk modulus and p is the density of the medium,
?
is
the wavelength of the waves.
[Ans. incorrect]
7. Check the correctness of the relation,
3
4
g
p
Rg ?
?
, where the letters have their usual
meaning.
[Ans. correct]
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
8. The orbital velocity v of a satellite may depend on its mass m, the distance r form the
center of the earth and the acceleration due to gravity g. by the method of dimensional
analysis, obtain an expression of v.
[ . ] Ansv rg ?

9. A U-tube of uniform cross-section contains mercury up to a height h in either limb.
The mercury in one limb is depressed a little and then released. Obtain an expression
for the time period of oscillation.
[ . 2 ]
h
AnsT
g
? ?

10. Given the value of G in cgs system as 6.67X10
-8
dyne cm
2
/g
2
, find the value in mks
system in
22
/. Nm kg

11
[ .6.67 10 ] Ans
?
?

11. By the method of dimensions, show that energy per unit volume is dimensionally
equal to the pressure.
12. Express
46
3.0 10 1.7 10
??
? ? ?
with proper signification figures.
4
[ .3.0 10 ] Ans
?
?

13. The surface tent ion (T) is measured by capillary rise formula
2cos
rhpg
T
?
?
. The
quantities p.g and 0 are taken from the table of constants while height and diameter
are measured as h=(3.00+0.001)cm and D=(0.250+0.001)cm.find the percentage error
in T.
[Ans.07%)]
14. The period of oscillation of a simple pendulum is
2 1/ . Tg ? ?
The length
l
40cm and is known to 1 mm accuracy. The time of 50 oscillation is 80s measured with a
write watch of 1 s resolution. What is the error in the determination of g ?
[Ans.2.8%]
15. The radius of sphere is measured as (2.1+0.5)cm. calculate its surface area with
error limits.
2
[ .{(55.4 26.4) }] Ans cm ?

16. The voltage across  lamp is (6.0+0.1) volt and the current passing through it is
(4.0+0.2) ampere. Find the power consumed by the lamp.
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
[Ans.{(24.0+1.6)watt}]
17. The length and breadth of a rectangular block are 25.2cm and 16,8cm, which have
both been measured to an accuracy of 0.1cm. find the area of the rectangular block.
[Ans.{(423.4+4.2)cm
2
}]
18. A force of (2500+5) N is applied over an area of (0.32+0.02)m
2
. Calculate the
pressure exerted over the area.
[Ans.{(7812.5+503.9)N/m
2
}]
19. To find the value of g, by using a simple pendulum, the following observations were
made: length of the thread l=(100+0.1)cm, the period of oscillation T =(2+0.1)s
calculate the maximum permissible error in measurement of `g’ which quantity should
be measured more accurately and why?
[ .10.1%, 2 ]
g l T
Ans Tas
g l T
? ? ?
??

20. The radius of curvature of a concave mirror, measured by a spherometer, is given
by
2
62
lh
R
h
??
The value of l and h are 4.0cm and 0.065cm respectively, where l is
measured by a meter scale and h by a spherometer. Find the relative error in the
measurement of R.
[Ans.(0.08)]
21. In searle’s experiment the diameter of the wire, as measured by a screw gauge, of
least count 0.001cm, is 0.500cm. The length, measured by a scale of least count 0.1cm,
is 110.0cm, when a weight of 40N is suspended from the wire, its exertion is measured
to be 0.125 cm by a micrometer of least count 0.001cm. find the young’s modulus of
the material of the wire from this data.
11 9 2
[ .{(2.2 10 10.758 10 ) / }] Ans N m ? ? ?

22. A small error in the measurement of the quantity having the highest power (in a
given formula). Will contribute maximum percentage error in the value of the physical
quantity to whom it is related. Explain why?
[Ans. refer to art.3.6(c), page 56]
23. The two specific heat capacitates of a gas are measured as
(12.28 0.2) Cp??
units
and
(3.97 0.3) Cv??
units. Find the value of the
[Ans.{(8.31.0.5)units}]
Page 4

PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
XI ASSIGNMENT-1  : DIMENSION ANALYSIS & ERRORS
1. The velocity v of particle depends upon t according to the equation .
()
c
u a bt
dt
? ? ?
?
write the dimensions of a, b, c and d.
[Ans.
12
[ ],[ ],[ ],[ ]] LT LT L T
??

2. Write the dimension of ab is the relations
2
()
,
bx
E
at
?
?
where E is the energy, x is the
distance and t is the time.
[Ans.
12
[] M LT
?
]
3. Write the dimensions of (a/b) in the relation
2
()
,
at
p
bx
?
?
where P is the pressure, x is
the distance and t is the time.
[Ans.
2
[] MT
?
]
4. An apprentice engineer found that volume V of water which passes any point of
canal during time t is connected with the cross-section a of the canal and the velocity v
of water by the relation, V=kavt. Verify the correctness of the relation.
[Ans. Incorrect]
5. The height h to which a liquid of surface tent ion T and density p rises in a capillary of
radius r is given by the relation
2
2 cos T
h
rg
?
?
?
where
?
is the angle of contact and g is the
acceleration due to gravity. Verify the correctness of this statement.
[Ans. incorrect]
6. check the dimensional consistency of the formula,
1 B
u
p ?
?
,where v is the velocity of
the longitudinal waves, B is the bulk modulus and p is the density of the medium,
?
is
the wavelength of the waves.
[Ans. incorrect]
7. Check the correctness of the relation,
3
4
g
p
Rg ?
?
, where the letters have their usual
meaning.
[Ans. correct]
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
8. The orbital velocity v of a satellite may depend on its mass m, the distance r form the
center of the earth and the acceleration due to gravity g. by the method of dimensional
analysis, obtain an expression of v.
[ . ] Ansv rg ?

9. A U-tube of uniform cross-section contains mercury up to a height h in either limb.
The mercury in one limb is depressed a little and then released. Obtain an expression
for the time period of oscillation.
[ . 2 ]
h
AnsT
g
? ?

10. Given the value of G in cgs system as 6.67X10
-8
dyne cm
2
/g
2
, find the value in mks
system in
22
/. Nm kg

11
[ .6.67 10 ] Ans
?
?

11. By the method of dimensions, show that energy per unit volume is dimensionally
equal to the pressure.
12. Express
46
3.0 10 1.7 10
??
? ? ?
with proper signification figures.
4
[ .3.0 10 ] Ans
?
?

13. The surface tent ion (T) is measured by capillary rise formula
2cos
rhpg
T
?
?
. The
quantities p.g and 0 are taken from the table of constants while height and diameter
are measured as h=(3.00+0.001)cm and D=(0.250+0.001)cm.find the percentage error
in T.
[Ans.07%)]
14. The period of oscillation of a simple pendulum is
2 1/ . Tg ? ?
The length
l
40cm and is known to 1 mm accuracy. The time of 50 oscillation is 80s measured with a
write watch of 1 s resolution. What is the error in the determination of g ?
[Ans.2.8%]
15. The radius of sphere is measured as (2.1+0.5)cm. calculate its surface area with
error limits.
2
[ .{(55.4 26.4) }] Ans cm ?

16. The voltage across  lamp is (6.0+0.1) volt and the current passing through it is
(4.0+0.2) ampere. Find the power consumed by the lamp.
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
[Ans.{(24.0+1.6)watt}]
17. The length and breadth of a rectangular block are 25.2cm and 16,8cm, which have
both been measured to an accuracy of 0.1cm. find the area of the rectangular block.
[Ans.{(423.4+4.2)cm
2
}]
18. A force of (2500+5) N is applied over an area of (0.32+0.02)m
2
. Calculate the
pressure exerted over the area.
[Ans.{(7812.5+503.9)N/m
2
}]
19. To find the value of g, by using a simple pendulum, the following observations were
made: length of the thread l=(100+0.1)cm, the period of oscillation T =(2+0.1)s
calculate the maximum permissible error in measurement of `g’ which quantity should
be measured more accurately and why?
[ .10.1%, 2 ]
g l T
Ans Tas
g l T
? ? ?
??

20. The radius of curvature of a concave mirror, measured by a spherometer, is given
by
2
62
lh
R
h
??
The value of l and h are 4.0cm and 0.065cm respectively, where l is
measured by a meter scale and h by a spherometer. Find the relative error in the
measurement of R.
[Ans.(0.08)]
21. In searle’s experiment the diameter of the wire, as measured by a screw gauge, of
least count 0.001cm, is 0.500cm. The length, measured by a scale of least count 0.1cm,
is 110.0cm, when a weight of 40N is suspended from the wire, its exertion is measured
to be 0.125 cm by a micrometer of least count 0.001cm. find the young’s modulus of
the material of the wire from this data.
11 9 2
[ .{(2.2 10 10.758 10 ) / }] Ans N m ? ? ?

22. A small error in the measurement of the quantity having the highest power (in a
given formula). Will contribute maximum percentage error in the value of the physical
quantity to whom it is related. Explain why?
[Ans. refer to art.3.6(c), page 56]
23. The two specific heat capacitates of a gas are measured as
(12.28 0.2) Cp??
units
and
(3.97 0.3) Cv??
units. Find the value of the
[Ans.{(8.31.0.5)units}]
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
24. The period of oscillation of a compound pendulum is given by
22
2
kl
t
lg
?
?
?
where l
is distance of the point of suspension from is CG and k is the radius of gyration of the
pendulum about a parallel axis through CG. Test the validity of the above equation by
the method of dimensions.
[Ans. Correct]
25. A flywheel of moment of inertia l is set into rotation by the descent of a mass m. if
?
is the angular velocity of the flywheel and v is
22
11
22
mgh mv l ? ??
.
Show by your knowledge of dimensions that is equation is correct.
26. Test by method of dimensions the correctness of the equation,
3
3
4
mgl
bd y
? ?

Where
?
is the depression produced at the centre of a bar of length l, breadth b and
depth d, placed symmetrically on two knife edges near its ends and loaded in the
middle by a mass m, and Y is the young’s modulus of the material of the bar.
[Ans. correct]
27. Speed (v) of sound in a medium of elasticity E and density p is given by v=
/. Ep
check the accuracy of the above statement.
[Ans. Correct]
28. Check the dimensional accuracy of the relation
2
1
2
mv mgh ?
where the letters have
their usual meaning.
[Ans. correct]
29. Check by the method of dimensional the validity of the expression,
4
Pr
8
Q
l
?
?
?
where
Q is the volume of a liquid of viscosity n flowing per second through a capillary tube of
length l and radius r and the pressure difference between the end of the tube it P.
[Ans. Correct]

30. A student claims that the time t of tree fall of a body depends upon the height h
from which it falls, the mass m of the body and the acceleration due to gravity g. use
the method of dimensional to check his claim.
[Ans. Claim is partly correct]
Page 5

PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
XI ASSIGNMENT-1  : DIMENSION ANALYSIS & ERRORS
1. The velocity v of particle depends upon t according to the equation .
()
c
u a bt
dt
? ? ?
?
write the dimensions of a, b, c and d.
[Ans.
12
[ ],[ ],[ ],[ ]] LT LT L T
??

2. Write the dimension of ab is the relations
2
()
,
bx
E
at
?
?
where E is the energy, x is the
distance and t is the time.
[Ans.
12
[] M LT
?
]
3. Write the dimensions of (a/b) in the relation
2
()
,
at
p
bx
?
?
where P is the pressure, x is
the distance and t is the time.
[Ans.
2
[] MT
?
]
4. An apprentice engineer found that volume V of water which passes any point of
canal during time t is connected with the cross-section a of the canal and the velocity v
of water by the relation, V=kavt. Verify the correctness of the relation.
[Ans. Incorrect]
5. The height h to which a liquid of surface tent ion T and density p rises in a capillary of
radius r is given by the relation
2
2 cos T
h
rg
?
?
?
where
?
is the angle of contact and g is the
acceleration due to gravity. Verify the correctness of this statement.
[Ans. incorrect]
6. check the dimensional consistency of the formula,
1 B
u
p ?
?
,where v is the velocity of
the longitudinal waves, B is the bulk modulus and p is the density of the medium,
?
is
the wavelength of the waves.
[Ans. incorrect]
7. Check the correctness of the relation,
3
4
g
p
Rg ?
?
, where the letters have their usual
meaning.
[Ans. correct]
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
8. The orbital velocity v of a satellite may depend on its mass m, the distance r form the
center of the earth and the acceleration due to gravity g. by the method of dimensional
analysis, obtain an expression of v.
[ . ] Ansv rg ?

9. A U-tube of uniform cross-section contains mercury up to a height h in either limb.
The mercury in one limb is depressed a little and then released. Obtain an expression
for the time period of oscillation.
[ . 2 ]
h
AnsT
g
? ?

10. Given the value of G in cgs system as 6.67X10
-8
dyne cm
2
/g
2
, find the value in mks
system in
22
/. Nm kg

11
[ .6.67 10 ] Ans
?
?

11. By the method of dimensions, show that energy per unit volume is dimensionally
equal to the pressure.
12. Express
46
3.0 10 1.7 10
??
? ? ?
with proper signification figures.
4
[ .3.0 10 ] Ans
?
?

13. The surface tent ion (T) is measured by capillary rise formula
2cos
rhpg
T
?
?
. The
quantities p.g and 0 are taken from the table of constants while height and diameter
are measured as h=(3.00+0.001)cm and D=(0.250+0.001)cm.find the percentage error
in T.
[Ans.07%)]
14. The period of oscillation of a simple pendulum is
2 1/ . Tg ? ?
The length
l
40cm and is known to 1 mm accuracy. The time of 50 oscillation is 80s measured with a
write watch of 1 s resolution. What is the error in the determination of g ?
[Ans.2.8%]
15. The radius of sphere is measured as (2.1+0.5)cm. calculate its surface area with
error limits.
2
[ .{(55.4 26.4) }] Ans cm ?

16. The voltage across  lamp is (6.0+0.1) volt and the current passing through it is
(4.0+0.2) ampere. Find the power consumed by the lamp.
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
[Ans.{(24.0+1.6)watt}]
17. The length and breadth of a rectangular block are 25.2cm and 16,8cm, which have
both been measured to an accuracy of 0.1cm. find the area of the rectangular block.
[Ans.{(423.4+4.2)cm
2
}]
18. A force of (2500+5) N is applied over an area of (0.32+0.02)m
2
. Calculate the
pressure exerted over the area.
[Ans.{(7812.5+503.9)N/m
2
}]
19. To find the value of g, by using a simple pendulum, the following observations were
made: length of the thread l=(100+0.1)cm, the period of oscillation T =(2+0.1)s
calculate the maximum permissible error in measurement of `g’ which quantity should
be measured more accurately and why?
[ .10.1%, 2 ]
g l T
Ans Tas
g l T
? ? ?
??

20. The radius of curvature of a concave mirror, measured by a spherometer, is given
by
2
62
lh
R
h
??
The value of l and h are 4.0cm and 0.065cm respectively, where l is
measured by a meter scale and h by a spherometer. Find the relative error in the
measurement of R.
[Ans.(0.08)]
21. In searle’s experiment the diameter of the wire, as measured by a screw gauge, of
least count 0.001cm, is 0.500cm. The length, measured by a scale of least count 0.1cm,
is 110.0cm, when a weight of 40N is suspended from the wire, its exertion is measured
to be 0.125 cm by a micrometer of least count 0.001cm. find the young’s modulus of
the material of the wire from this data.
11 9 2
[ .{(2.2 10 10.758 10 ) / }] Ans N m ? ? ?

22. A small error in the measurement of the quantity having the highest power (in a
given formula). Will contribute maximum percentage error in the value of the physical
quantity to whom it is related. Explain why?
[Ans. refer to art.3.6(c), page 56]
23. The two specific heat capacitates of a gas are measured as
(12.28 0.2) Cp??
units
and
(3.97 0.3) Cv??
units. Find the value of the
[Ans.{(8.31.0.5)units}]
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
24. The period of oscillation of a compound pendulum is given by
22
2
kl
t
lg
?
?
?
where l
is distance of the point of suspension from is CG and k is the radius of gyration of the
pendulum about a parallel axis through CG. Test the validity of the above equation by
the method of dimensions.
[Ans. Correct]
25. A flywheel of moment of inertia l is set into rotation by the descent of a mass m. if
?
is the angular velocity of the flywheel and v is
22
11
22
mgh mv l ? ??
.
Show by your knowledge of dimensions that is equation is correct.
26. Test by method of dimensions the correctness of the equation,
3
3
4
mgl
bd y
? ?

Where
?
is the depression produced at the centre of a bar of length l, breadth b and
depth d, placed symmetrically on two knife edges near its ends and loaded in the
middle by a mass m, and Y is the young’s modulus of the material of the bar.
[Ans. correct]
27. Speed (v) of sound in a medium of elasticity E and density p is given by v=
/. Ep
check the accuracy of the above statement.
[Ans. Correct]
28. Check the dimensional accuracy of the relation
2
1
2
mv mgh ?
where the letters have
their usual meaning.
[Ans. correct]
29. Check by the method of dimensional the validity of the expression,
4
Pr
8
Q
l
?
?
?
where
Q is the volume of a liquid of viscosity n flowing per second through a capillary tube of
length l and radius r and the pressure difference between the end of the tube it P.
[Ans. Correct]

30. A student claims that the time t of tree fall of a body depends upon the height h
from which it falls, the mass m of the body and the acceleration due to gravity g. use
the method of dimensional to check his claim.
[Ans. Claim is partly correct]
PHYSICS CLASSES
by Puneet kr.
XI/XII/ ENGINEERING/MEDICAL ENTRANCE EXAM
98/A-1, FIRST FLOOR, SECTOR-6, ROHINI                                       9810 35 05 01/ 9582 432 479
31. Derive the relation E=mc
2
using the method of dimensional.
32. Derive by the method of dimensional, an expression for the energy of a body
executing SHM, assuming that this energy depends upon : (i) the mass m (ii) the
frequency v (iii) the amplitude of vibration r.
[Ans. E=km v
2
r
2
]
33. Assuming that the mass m of the largest stone that can be moved by a flowing river
gravity), show that m varies with sixth power of the velocity of flow.
34. Show dimensional that the centripetal force acting on a particle of mass m moving
in a circle of radius r with a uniform speed of v rotations per second is
22
4. v mr ?

35. A gas bubble from an explosion under water oscillates with a period T proportional
to P
a
p
b
E
c
where p is the static pressure, p is the density of water and E is the total
energy of the explosion. Find the values of a,b and c.
[Ans.a=-5/6,b=1/2, c=1/3]
36. A jet of water of cross-sectional area a impinges normally on a stationary flat plate
with a velocity v. if p is the density of water determine by dimensional analysis the
expression for the force, F exerted by the jet on the plate.
2
[ . ] AnsF kav p ?

37. If the depth d to which bullet of kinetic energy K  can penetrate into a human body
of elasticity E, using the method of dimensions, establish a relation between d, K and E.
1/3
[ . ( / ) ] Ansd K E ?

38. Obtain by the method of dimensional analysis, an expression for the surface tention
(S) of a liquid rising in a capillary tube. Assume that the surface tension depends upon :
(i) mass (m) of the liquid (ii) pressure (p) of the liquid and (iii) radius (r) of the capillary
tube. The constant of proportionality, k=1/2.
[Ans.S=rp/2
39. A large fluid star oscillates in shape under the influence of its own gravitational
field. Using the method of dimensions, obtain an expression for the period of oscillation
(T) in terms of radius (R) of the star, its mean density (p) and universal gravitational
constant (G).
[ . / ] AnsT k pG ?

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