Measurements (Errors) Practice Questions - DPP for NEET

 Page 1


Q.1 A wire has a mass 0.3 ± 0.003g, radius 0.5 ± 0.005 mm and
length 6 ± 0.06 cm. The maximum percentage error in the
measurement of its density is
(a)1 (b)2 (c)3 (d)4
Q.2 If 97.52 is divided by 2.54, the correct result in terms of
significant figures is
(a) 38.4 (b) 38.3937
(c) 38.394 (d) 38.39
Q.3 A physical quantity A is related to four observable a, b, c
and d as follows, 
23
=
ab
A
cd
 the percentage errors of
measurement in a, b, c and d are 1%, 3%, 2% and 2%
respectiely . What is the percentage error in the quantity A
(a) 12% (b) 7%
(c) 5% (d) 14%
Q.4 A physical quantity is given by . =
a bc
X M LT The
percentage error in measurement of M, L and T are  a, b and
g respectively. Then maximum percentage error in the
quantity X is
(a)aa+ bb + cg (b) aa+ bb – cg
(c) ++
a bg
a bc
(d) None of these
Page 2


Q.1 A wire has a mass 0.3 ± 0.003g, radius 0.5 ± 0.005 mm and
length 6 ± 0.06 cm. The maximum percentage error in the
measurement of its density is
(a)1 (b)2 (c)3 (d)4
Q.2 If 97.52 is divided by 2.54, the correct result in terms of
significant figures is
(a) 38.4 (b) 38.3937
(c) 38.394 (d) 38.39
Q.3 A physical quantity A is related to four observable a, b, c
and d as follows, 
23
=
ab
A
cd
 the percentage errors of
measurement in a, b, c and d are 1%, 3%, 2% and 2%
respectiely . What is the percentage error in the quantity A
(a) 12% (b) 7%
(c) 5% (d) 14%
Q.4 A physical quantity is given by . =
a bc
X M LT The
percentage error in measurement of M, L and T are  a, b and
g respectively. Then maximum percentage error in the
quantity X is
(a)aa+ bb + cg (b) aa+ bb – cg
(c) ++
a bg
a bc
(d) None of these
2
DPP/ P 02
Q.5 If the length of rod A is 3.25 ± 0.01 cm and that of B is
4.19 ± 0.01 cm then the rod B is longer than rod A by
(a) 0.94 ± 0.00 cm (b) 0.94 ± 0.01 cm
(c) 0.94 ± 0.02 cm (d) 0.94 ± 0.005 cm
Q.6 If L = 2.331 cm, B = 2.1 cm, then L + B =
(a) 4.431 cm (b) 4.43 cm
(c) 4.4 c m (d) 4 cm
Q.7 The number of significant figures in all the given numbers
25.12, 2009, 4.156 and 1.217 × 10
–4
 is
(a)1 (b)2 (c)3 (d)4
Q.8 In an experiment, the following observation's were
recorded: L = 2.820 m, M = 3.00 kg, l = 0.087 cm,
Diameter D = 0.041 cm. Taking g = 9.81 m/s
2
 using the
formula, 
2
4
, =
p
MgL
Y
Dl
the maximum percentage error in Y
is
(a) 7.96% (b) 4.56% (c) 6.50% (d) 8.42%
Q.9 A physical parameter a can be determined by measuring
the parameters b, c, d and e using the relation a = .
ab
gd
bc
de
If the maximum errors in the measurement of b, c, d and e
are b
1
%, c
1
%, d
1
%, and e
1
%, then the maximum error in
the value of a determined by the experiment is
(a) (b
1
+ c
1
+ d
1
+ e
1
)% (b) (b
1
+ c
1
– d
1
– e
1
)%
(c)(ab
1
+ bc
1
– gd
1
– de
1
)%(d) (ab
1
+ bc
1
+ gd
1
+ de
1
)%
Q.10 The period of oscillation of a simple pendulum is given by
2 =p
l
T
g
 where l is about 100 cm and is known to have
1mm accuracy. The period is about 2s. The time of 100
oscillations is measured by a stopwatch of least count 0.1s.
The percentage error in g is
(a) 0.1% (b) 1%
(c) 0.2% (d) 0.8%
Q.11 The mean time period of second's pendulum is 2.00s and
mean absolute error in the time period is 0.05s. To express
maximum estimate of error, the time period should be
written as
(a) (2.00 ± 0.01)s (b) (2.00 + 0.025) s
(c) (2.00 ± 0.05) s (d) (2.00 ± 0.10) s
Q.12 Error in the measurement of radius of a sphere is 1%. The
error in the calculated value of its volume is
(a) 1% (b) 3%
(c) 5% (d) 7%
Q.13The relative density of material of a body is found by
weighing it first in air and then in water. If the weight in air
is (5.00 ± 0.05) newton and weight in water is (4.00 ± 0.05)
newton. Then the relative density along with the maximum
permissible percentage error is
(a) 5.0 ± 11% (b) 5.0 ± 1%
(c) 5.0 ± 6% (d) 1.25 ± 5%
Q.14 The resistance =
V
R
i
 where V = 100 ± 5 volts and
i = 10 ± 0.2 amperes. What is the total error in R ?
(a) 5% (b) 7% (c) 5.2% (d)
5
%
2
Q.15 The length of a cylinder is measured with a meter rod having
least count 0.1 cm. Its diameter is measured with vernier
calipers having least count 0.01 cm. Given that length is
5.0 cm. and radius is 2.0 cm. The percentage error in the
calculated value of the volume will be
(a) 1% (b) 2%
(c) 3% (d) 4%
Q.16 According to Joule’s law of heating, heat produced H =
I
2
Rt, where I is current, R is resistance and t is time . If the
errors in the measurements of I,R. and t are 3%, 4% and
6% respectively then error in the measurement of H is
(a) ± 17% (b) ± 16%
(c) ± 19% (d) ± 25%
Page 3


Q.1 A wire has a mass 0.3 ± 0.003g, radius 0.5 ± 0.005 mm and
length 6 ± 0.06 cm. The maximum percentage error in the
measurement of its density is
(a)1 (b)2 (c)3 (d)4
Q.2 If 97.52 is divided by 2.54, the correct result in terms of
significant figures is
(a) 38.4 (b) 38.3937
(c) 38.394 (d) 38.39
Q.3 A physical quantity A is related to four observable a, b, c
and d as follows, 
23
=
ab
A
cd
 the percentage errors of
measurement in a, b, c and d are 1%, 3%, 2% and 2%
respectiely . What is the percentage error in the quantity A
(a) 12% (b) 7%
(c) 5% (d) 14%
Q.4 A physical quantity is given by . =
a bc
X M LT The
percentage error in measurement of M, L and T are  a, b and
g respectively. Then maximum percentage error in the
quantity X is
(a)aa+ bb + cg (b) aa+ bb – cg
(c) ++
a bg
a bc
(d) None of these
2
DPP/ P 02
Q.5 If the length of rod A is 3.25 ± 0.01 cm and that of B is
4.19 ± 0.01 cm then the rod B is longer than rod A by
(a) 0.94 ± 0.00 cm (b) 0.94 ± 0.01 cm
(c) 0.94 ± 0.02 cm (d) 0.94 ± 0.005 cm
Q.6 If L = 2.331 cm, B = 2.1 cm, then L + B =
(a) 4.431 cm (b) 4.43 cm
(c) 4.4 c m (d) 4 cm
Q.7 The number of significant figures in all the given numbers
25.12, 2009, 4.156 and 1.217 × 10
–4
 is
(a)1 (b)2 (c)3 (d)4
Q.8 In an experiment, the following observation's were
recorded: L = 2.820 m, M = 3.00 kg, l = 0.087 cm,
Diameter D = 0.041 cm. Taking g = 9.81 m/s
2
 using the
formula, 
2
4
, =
p
MgL
Y
Dl
the maximum percentage error in Y
is
(a) 7.96% (b) 4.56% (c) 6.50% (d) 8.42%
Q.9 A physical parameter a can be determined by measuring
the parameters b, c, d and e using the relation a = .
ab
gd
bc
de
If the maximum errors in the measurement of b, c, d and e
are b
1
%, c
1
%, d
1
%, and e
1
%, then the maximum error in
the value of a determined by the experiment is
(a) (b
1
+ c
1
+ d
1
+ e
1
)% (b) (b
1
+ c
1
– d
1
– e
1
)%
(c)(ab
1
+ bc
1
– gd
1
– de
1
)%(d) (ab
1
+ bc
1
+ gd
1
+ de
1
)%
Q.10 The period of oscillation of a simple pendulum is given by
2 =p
l
T
g
 where l is about 100 cm and is known to have
1mm accuracy. The period is about 2s. The time of 100
oscillations is measured by a stopwatch of least count 0.1s.
The percentage error in g is
(a) 0.1% (b) 1%
(c) 0.2% (d) 0.8%
Q.11 The mean time period of second's pendulum is 2.00s and
mean absolute error in the time period is 0.05s. To express
maximum estimate of error, the time period should be
written as
(a) (2.00 ± 0.01)s (b) (2.00 + 0.025) s
(c) (2.00 ± 0.05) s (d) (2.00 ± 0.10) s
Q.12 Error in the measurement of radius of a sphere is 1%. The
error in the calculated value of its volume is
(a) 1% (b) 3%
(c) 5% (d) 7%
Q.13The relative density of material of a body is found by
weighing it first in air and then in water. If the weight in air
is (5.00 ± 0.05) newton and weight in water is (4.00 ± 0.05)
newton. Then the relative density along with the maximum
permissible percentage error is
(a) 5.0 ± 11% (b) 5.0 ± 1%
(c) 5.0 ± 6% (d) 1.25 ± 5%
Q.14 The resistance =
V
R
i
 where V = 100 ± 5 volts and
i = 10 ± 0.2 amperes. What is the total error in R ?
(a) 5% (b) 7% (c) 5.2% (d)
5
%
2
Q.15 The length of a cylinder is measured with a meter rod having
least count 0.1 cm. Its diameter is measured with vernier
calipers having least count 0.01 cm. Given that length is
5.0 cm. and radius is 2.0 cm. The percentage error in the
calculated value of the volume will be
(a) 1% (b) 2%
(c) 3% (d) 4%
Q.16 According to Joule’s law of heating, heat produced H =
I
2
Rt, where I is current, R is resistance and t is time . If the
errors in the measurements of I,R. and t are 3%, 4% and
6% respectively then error in the measurement of H is
(a) ± 17% (b) ± 16%
(c) ± 19% (d) ± 25%
DPP/ P 02
3
Q.17 A physical quantity P is given by 
1
3
2
3
4
2
.
-
=
AB
P
CD
 The quantity
which brings in the maximum percentage error in P is
(a)A (b)B
(c)C (d)D
Q.18If there is a positive error of 50% in the measurement of
velocity of a body, then the error in the measurement of
kinetic energy is
(a) 25% (b) 50%
(c) 100% (d) 125%
Q.19The random error in the arithmetic mean of 100
observations is x; then random error in the arithmetic mean
of 400 observations would be
(a)4x (b)
1
4
x (c)2x (d)
1
2
x
Q.20The percentage errors in the measurement of mass and
speed are 2% and 3% respectively. How much will be the
maximum error in the estimation of the kinetic energy
obtained by measuring mass and speed?
(a) 11% (b) 8%
(c) 5% (d) 1%
Q.21 The unit of percentage error is
(a) Same as that of physical quantity
(b) Different from that of physical quantity
(c) Percentage error is unitless
(d) Errors have got their own units which are different
from that of physical quantity measured
DIRECTIONS (Q.22-Q.24) : In the following questions,
more than one of the answers  given are correct. Select the
correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.22 In the context of accuracy of measurement and significant
figures in expressing results of experiment, which of the
following is/are correct?
1. Out of the two measurements 50.14 cm and 0.00025
ampere, the first one has greater accuracy
2. Out of the two measurements 50.14 cm and 0.00025
ampere, the second has greater accuracy.
3. If one travels 478 km by rail and 397 m by road, the
total distance travelled is 875 km.
4. If one travels 697 m by rail and 478 km by road, the
total distance is 478 km.
Q.23 A thin copper wire of length l metre increases in length by
2% when heated through 10°C. Which is not the
percentage increase in area when a square copper sheet of
length l metre is heated through 10°C
(1) 12% (2) 8% (3) 16% (4) 4%
Q.24 A body travels uniformly a distance of (13.8 ± 0.2) m in a
time (4.0 ± 0.3) s.
1. Its velocity with error limit is (3.5 0.31) ± ms
–1
2. Its velocity with error limit is (3.5 0.11) ± ms
–1
3. Percentage error in velocity is 4% ±
4. Percentage error in velocity is 9% ±
DIRECTION (Q.25-Q.27) : Read the passage given below
and answer the questions that follows :
The internal radius of a 1m long resonance tube is measured as
3 cm. A tuning fork of frequency 2000 Hz is used. The first
resonating length is measured as 4.6 cm and the second
resonating length is measured as 14.0 cm.
Q.25 Calculate the maximum percentage error in measurement
of e.
(a) 3.33% (b)  2.23% (c) 4.33% (d)  5.33%
Q.26 Calculate the speed of sound at the room temperature.
(a) 275 m/s (b)  376 m/s
(c) 356 m/s (d)  330 m/s
Page 4


Q.1 A wire has a mass 0.3 ± 0.003g, radius 0.5 ± 0.005 mm and
length 6 ± 0.06 cm. The maximum percentage error in the
measurement of its density is
(a)1 (b)2 (c)3 (d)4
Q.2 If 97.52 is divided by 2.54, the correct result in terms of
significant figures is
(a) 38.4 (b) 38.3937
(c) 38.394 (d) 38.39
Q.3 A physical quantity A is related to four observable a, b, c
and d as follows, 
23
=
ab
A
cd
 the percentage errors of
measurement in a, b, c and d are 1%, 3%, 2% and 2%
respectiely . What is the percentage error in the quantity A
(a) 12% (b) 7%
(c) 5% (d) 14%
Q.4 A physical quantity is given by . =
a bc
X M LT The
percentage error in measurement of M, L and T are  a, b and
g respectively. Then maximum percentage error in the
quantity X is
(a)aa+ bb + cg (b) aa+ bb – cg
(c) ++
a bg
a bc
(d) None of these
2
DPP/ P 02
Q.5 If the length of rod A is 3.25 ± 0.01 cm and that of B is
4.19 ± 0.01 cm then the rod B is longer than rod A by
(a) 0.94 ± 0.00 cm (b) 0.94 ± 0.01 cm
(c) 0.94 ± 0.02 cm (d) 0.94 ± 0.005 cm
Q.6 If L = 2.331 cm, B = 2.1 cm, then L + B =
(a) 4.431 cm (b) 4.43 cm
(c) 4.4 c m (d) 4 cm
Q.7 The number of significant figures in all the given numbers
25.12, 2009, 4.156 and 1.217 × 10
–4
 is
(a)1 (b)2 (c)3 (d)4
Q.8 In an experiment, the following observation's were
recorded: L = 2.820 m, M = 3.00 kg, l = 0.087 cm,
Diameter D = 0.041 cm. Taking g = 9.81 m/s
2
 using the
formula, 
2
4
, =
p
MgL
Y
Dl
the maximum percentage error in Y
is
(a) 7.96% (b) 4.56% (c) 6.50% (d) 8.42%
Q.9 A physical parameter a can be determined by measuring
the parameters b, c, d and e using the relation a = .
ab
gd
bc
de
If the maximum errors in the measurement of b, c, d and e
are b
1
%, c
1
%, d
1
%, and e
1
%, then the maximum error in
the value of a determined by the experiment is
(a) (b
1
+ c
1
+ d
1
+ e
1
)% (b) (b
1
+ c
1
– d
1
– e
1
)%
(c)(ab
1
+ bc
1
– gd
1
– de
1
)%(d) (ab
1
+ bc
1
+ gd
1
+ de
1
)%
Q.10 The period of oscillation of a simple pendulum is given by
2 =p
l
T
g
 where l is about 100 cm and is known to have
1mm accuracy. The period is about 2s. The time of 100
oscillations is measured by a stopwatch of least count 0.1s.
The percentage error in g is
(a) 0.1% (b) 1%
(c) 0.2% (d) 0.8%
Q.11 The mean time period of second's pendulum is 2.00s and
mean absolute error in the time period is 0.05s. To express
maximum estimate of error, the time period should be
written as
(a) (2.00 ± 0.01)s (b) (2.00 + 0.025) s
(c) (2.00 ± 0.05) s (d) (2.00 ± 0.10) s
Q.12 Error in the measurement of radius of a sphere is 1%. The
error in the calculated value of its volume is
(a) 1% (b) 3%
(c) 5% (d) 7%
Q.13The relative density of material of a body is found by
weighing it first in air and then in water. If the weight in air
is (5.00 ± 0.05) newton and weight in water is (4.00 ± 0.05)
newton. Then the relative density along with the maximum
permissible percentage error is
(a) 5.0 ± 11% (b) 5.0 ± 1%
(c) 5.0 ± 6% (d) 1.25 ± 5%
Q.14 The resistance =
V
R
i
 where V = 100 ± 5 volts and
i = 10 ± 0.2 amperes. What is the total error in R ?
(a) 5% (b) 7% (c) 5.2% (d)
5
%
2
Q.15 The length of a cylinder is measured with a meter rod having
least count 0.1 cm. Its diameter is measured with vernier
calipers having least count 0.01 cm. Given that length is
5.0 cm. and radius is 2.0 cm. The percentage error in the
calculated value of the volume will be
(a) 1% (b) 2%
(c) 3% (d) 4%
Q.16 According to Joule’s law of heating, heat produced H =
I
2
Rt, where I is current, R is resistance and t is time . If the
errors in the measurements of I,R. and t are 3%, 4% and
6% respectively then error in the measurement of H is
(a) ± 17% (b) ± 16%
(c) ± 19% (d) ± 25%
DPP/ P 02
3
Q.17 A physical quantity P is given by 
1
3
2
3
4
2
.
-
=
AB
P
CD
 The quantity
which brings in the maximum percentage error in P is
(a)A (b)B
(c)C (d)D
Q.18If there is a positive error of 50% in the measurement of
velocity of a body, then the error in the measurement of
kinetic energy is
(a) 25% (b) 50%
(c) 100% (d) 125%
Q.19The random error in the arithmetic mean of 100
observations is x; then random error in the arithmetic mean
of 400 observations would be
(a)4x (b)
1
4
x (c)2x (d)
1
2
x
Q.20The percentage errors in the measurement of mass and
speed are 2% and 3% respectively. How much will be the
maximum error in the estimation of the kinetic energy
obtained by measuring mass and speed?
(a) 11% (b) 8%
(c) 5% (d) 1%
Q.21 The unit of percentage error is
(a) Same as that of physical quantity
(b) Different from that of physical quantity
(c) Percentage error is unitless
(d) Errors have got their own units which are different
from that of physical quantity measured
DIRECTIONS (Q.22-Q.24) : In the following questions,
more than one of the answers  given are correct. Select the
correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.22 In the context of accuracy of measurement and significant
figures in expressing results of experiment, which of the
following is/are correct?
1. Out of the two measurements 50.14 cm and 0.00025
ampere, the first one has greater accuracy
2. Out of the two measurements 50.14 cm and 0.00025
ampere, the second has greater accuracy.
3. If one travels 478 km by rail and 397 m by road, the
total distance travelled is 875 km.
4. If one travels 697 m by rail and 478 km by road, the
total distance is 478 km.
Q.23 A thin copper wire of length l metre increases in length by
2% when heated through 10°C. Which is not the
percentage increase in area when a square copper sheet of
length l metre is heated through 10°C
(1) 12% (2) 8% (3) 16% (4) 4%
Q.24 A body travels uniformly a distance of (13.8 ± 0.2) m in a
time (4.0 ± 0.3) s.
1. Its velocity with error limit is (3.5 0.31) ± ms
–1
2. Its velocity with error limit is (3.5 0.11) ± ms
–1
3. Percentage error in velocity is 4% ±
4. Percentage error in velocity is 9% ±
DIRECTION (Q.25-Q.27) : Read the passage given below
and answer the questions that follows :
The internal radius of a 1m long resonance tube is measured as
3 cm. A tuning fork of frequency 2000 Hz is used. The first
resonating length is measured as 4.6 cm and the second
resonating length is measured as 14.0 cm.
Q.25 Calculate the maximum percentage error in measurement
of e.
(a) 3.33% (b)  2.23% (c) 4.33% (d)  5.33%
Q.26 Calculate the speed of sound at the room temperature.
(a) 275 m/s (b)  376 m/s
(c) 356 m/s (d)  330 m/s
4
DPP/ P 02
Q.27 Calculate the end correction.
(a) 0.2 cm (b)  0.3 cm
(c) 0.1 cm (d)  0.4 cm
DIRECTIONS (Q. 28-Q.30) : Each of these questions contains
two statements: Statement-1 (Assertion) and Statement-2
(Reason). Each of these questions has four alternative choices,
only one of which is the correct answer. You have to select the
correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement-1 is False, Statement-2 is True.
(d) Statement-1 is True, Statement-2 is False.
Q.28 Statement-1:  Number of significant figures in 0.005 is
one and that in 0.500 is three.
Statement-2 :  This is because zero is not significant.
Q.29 Statement-1:  Out of three measurements l = 0.7 m;
l = 0.70 m and l = 0.700 m, the last one is most accurate.
Statement-2: In every measurement, only the last
significant digit is not accurately known.
Q.30 Statement-1:  Parallex method cannot be used for
measuring distances of stars more than 100 light years
away.
Statement-2: Because parallex angle reduces so much that
it cannot be measured accurately.