Both numerically and dimensionally correct

Neither numerically nor dimensionally correct

JEE Questions for Physics Units And Measurements Quiz 14

The dimension of K in the equation W = 1/2 Kx² is

0%
0%
2)
0%
0%

Frequency is the function of density (ρ), length (a) and surface tension (T). Then its value is

0%
0%
2)
0%
0%
None of these

The dimensions of electric potential are

0%
0%
2)
0%
0%

Dimensions of potential energy are

0%
0%
2)
0%
0%

In the force (F), length (L) and time (T) are assumed to be fundamental units, then the dimensional formula of the mass will be

0%
0%
2)
0%
0%

In the relation y = a cos(ωt – kx), the dimensional formula for k is

0%
0%
2)
0%
0%

Position of a body with acceleration \'a\' is given by x = Ka^mtⁿ, here t is time. Find dimensions of m and n.

0%
m = 1, n = 1
0%
m = 1, n = 2
0%
m = 2, n = 1
0%
m = 2, n = 2

In a system of units if force (F), acceleration (A) and time (T) are taken as fundamental units, then the dimensional formula of energy is

0%
FA2T
0%
FAT2
0%
F2AT
0%
FAT

The dimensions of potential are the same as that of

0%
Work
0%
Electric field per unit charge
0%
Work per unit charge
0%
Force per unit charge

Physics-Units and Measurements-94044.png

0%
0.1%
0%
1%
0%
0.2%
0%
0.8%

The 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?

0%
11%
0%
8%
0%
5%
0%
1%

The random error in the arithmetic mean of 100 observation is x; then random error in the arithmetic mean of 400 observation would be

0%
4x
0%
1/4 x
0%
2x
0%
1/2 x

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree (= 0.5^o), then the least count of the instrument is

0%
One minute
0%
Half minute
0%
One degree
0%
Half degree

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further it is found that the screw gauge has zero error of –0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

0%
3.73 mm
0%
3.67 mm
0%
3.38 mm
0%
3.32 mm

Te mean time period of second\'s pendulum is 2.00 s and mean absolute error in the time period is 0.05 s. To express maximum estimate of error, the time period should be written as

0%
(2.00 ± 0.01)s
0%
(2.00 + 0.025)s
0%
(2.00 ± 0.05)s
0%
(2.00 ± 0.10)s

A body travels uniformly a distance of (13.8 ± 0.m in a time (4.0 ± 0.s. The velocity of the body within error limits is

0%
(3.45 ± 0.ms–1
0%
(3.45 ± 0.ms–1
0%
(3.45 ± 0.ms–1
0%
(3.45 ± 0.ms–1

The percentage error in the above problem is

0%
7%
0%
5.95%
0%
8.95%
0%
9.85%

The unit of percentage error is

0%
Same as that of physical quantity
0%
Different from that of physical quantity
0%
Percentage error is unit less
0%
Errors have got their own units which are different from that of physical quantity measured

Physics-Units and Measurements-94052.png

0%
a
0%
b
0%
c
0%
d

A thin copper wire of length l metre increases in length by 2% when heated through 10^oC. What is the percentage increases in area when a square copper sheet off length l metre is heated through 10^oC?

0%
45
0%
8%
0%
16%
0%
None of these

In the context of accuracy of measurement and significant figures in expressing results of experiment. Which of the following is/are correct?
I. Out of the two measurements 50.14 cm and 0.00025 ampere, the first one has greater accuracy
II. If one travels 478 km by rail and 397 m by road, the total distance traveled is 478 km.

0%
Only (I) is correct
0%
Only (II) is correct
0%
Both are correct
0%
None of the above is correct

Physics-Units and Measurements-94054.png

0%
0%
2)
0%
0%

The 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.newton and weight in water is (4.00 ± 0.newton. Then, the relative density along with the maximum permissible percentage error is

0%
5.0 ± 11%
0%
5.0 ± 1%
0%
5.0 ± 6%
0%
1.25 ± 5%

The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s respectively. The average absolute error is

0%
0.1 s
0%
0.11 s
0%
0.01 s
0%
1.0 s

The length of a cylinder is measured with a metre rod having least count 0.1 cm. Its diameter is measured with vernier callipers 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

0%
1%
0%
2%
0%
3%
0%
4%

Physics-Units and Measurements-94063.png

0%
7.96%
0%
4.56%
0%
6.50%
0%
8.42%

According to Joule\'s law of heating, heat produced H = I²Rt, where I is current, R is resistance and t is time. If the errors in the measurement of I, R and t are 3%, 4% and 6% respectively, then in the measurement of H is

0%
±17%
0%
±16%
0%
±19%
0%
±25%

Physics-Units and Measurements-94067.png

0%
A
0%
B
0%
C
0%
D

if L = 2.331 cm, B = 2.1 cm, then L + B is equal to

0%
4.431 cm
0%
4.43 cm
0%
4.4 cm
0%
4 cm

The number of significant figures in all the given numbers 25.12, 2009, 4.156 and 217 × 10^–4 is

0%
1
0%
2
0%
3
0%
4

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

0%
0.94 ± 0.00 cm
0%
0.94 ± 0.01 cm
0%
0.94 ± 0.02 cm
0%
0.94 ± 0.005 cm

A physical quantity is given by X = M^aL^bT^c. The percentage error in measurement of M, L and T are α, β and γ respectively. Then, maximum percentage error in the quantity X is

0%
0%
2)
0%
0%
None of these

Physics-Units and Measurements-94073.png

0%
12%
0%
7%
0%
5%
0%
14%

In an experiment, to measure the height of a bridge by dropping stone into underneath, if the error in measurement of time is 0.1 s at end of 2s, then the error in estimation of height of bridge will be

0%
0.49 m
0%
0.98 m
0%
1.96 m
0%
2.12 m

The values of two resistors are R₁ = (6 ± 0.3)kΩ and R₂ = (10 ± 0.2)kΩ. The percentage error in the equivalent resistance when they are connected in parallel is

0%
5.1255
0%
2%
0%
10.125%
0%
7%

A vernier callipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. for this Vernier callipers, the least count is

0%
0.02 mm
0%
0.05 mm
0%
0.1 mm
0%
0.2 mm

The respective number of significant figures for the numbers 23.023, 0..0003 and 2.1 × 10^–3 are

0%
4, 4, 2
0%
5, 1, 2
0%
5, 1, 5
0%
5, 5, 2

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 divisions. If the measured mass of the ball has a relative error of 20%, the relative percentage error in the density is

0%
0.9%
0%
2.4%
0%
3.1%
0%
4.2%

A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading : 0 mm
Circular scale reading : 52 divisions
Given that 1 mm o main scale corresponds to 100 divisions of the circular scale
The diameter of wire from the above data is

0%
0.52 cm
0%
0.052 cm
0%
0.026 cm
0%
0.005 cm

The mass and volume of a body are found to be 5.00 ± 0.05 kg and 1.00 ± 0.05 cm³ respectively. Then, the maximum possible percentage error in its density is

0%
6%
0%
3%
0%
10%
0%
5%
0%
7%

In the determination of Young\'s modulus Y = 5MLg/πld² using Searle\'s method, a wire of length L = 2m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurements

0%
Due to the errors in the measurement of d and l are the same
0%
Due to the error in the measurement of d is twice that due to the error in the measurement of l
0%
Due to the error in the measurement of l is twice that due to the error in the measurement of d
0%
Due to the error in the measurement of d is four times that due to the error in the measurement of l

A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading : 58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

0%
58.59 degree
0%
58.77 degree
0%
58.65 degree
0%
59 degree

If the acceleration due to gravity is 10 ms^–2 and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is

0%
3,60,000
0%
72,000
0%
36,000
0%
1,29,600

If L, C and R represents inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency?

0%
0%
2)
0%
0%

Physics-Units and Measurements-94090.png

0%
0%
2)
0%
0%

Physics-Units and Measurements-94096.png

0%
Only numerically correct
0%
Only dimensionally correct
0%
Both numerically and dimensionally correct
0%
Neither numerically nor dimensionally correct

Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table.
Least count for length = 0.1 cm
Least count for time = 0.1s
Physics-Units and Measurements-94098.png

Physics-Units and Measurements-94098.png

0%
EI = 0
0%
EI is minimum
0%
EI = EII
0%
EII is maximum

A highly rigid cubical block A of small mass M and side L is fixed rigidly onto another cubical block B of the same dimensions and of low modulus of rigidity η such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A executes small oscillations. The time period of which is given by

0%
0%
2)
0%
0%

The speed of light (c), gravitational constant (G) and Planck\'s constant (h) are taken as the fundamental units in a system. The dimension of time in this new system should be