JEE Physics - Units & measurement Question Paper With Answer Key
Exam Duration: 60 Mins Total Questions : 50
Which of the following pairs of physical quantities does not have the same dimensions?
- (a)
Couple and angular momentum
- (b)
(pressure X Volume) and surface tension
- (c)
Torque and Impulse
- (d)
Parsec and Light year
The density of copper is 9 g/cc. In a unit system in which unit length is 5 cm and unit mass is 45 g, the density of copper is
- (a)
25
- (b)
\(81\over 25\)
- (c)
1
- (d)
625
If speed of light (c), acceleration due to gravity (g), pressure (p) are taken as fundamental units, the dimension of gravitational constant (G) are
- (a)
c0 gp-3
- (b)
c2 g3 p-2
- (c)
c0 g2 p-1
- (d)
c2 g2 p-2
If L has the dimensions of length; V that of potential and \({ \epsilon }_{ 0 }\) is the permittivity of free space, than the quantity \({ \epsilon }_{ 0 }LV\) have the dimensions of
- (a)
current
- (b)
charge
- (c)
resistance
- (d)
voltage
Two resistances are expressed as \({ R }_{ 1 }=(2 \pm 0.5) ohm\) and \({ R }_{ 2 }= (8 \pm0.5)\ ohm\). If they are connected in parallel, the net resistance has percentage error equal to
- (a)
32.25%
- (b)
10%
- (c)
25%
- (d)
41.25%
The angle of business \(\theta\) for a cyclist taking a curve is given by \(tan\ \theta={v^n\over rg}\), where symbols have their usual meaning. Then, value of n is equal to
- (a)
1
- (b)
3
- (c)
2
- (d)
4
If velocity of light c, gravitational constant G and Planck's constant h are chosen as fundamental units, then the dimensions of mass are
- (a)
\([h^{1/2}\ c^{1/2}\ G^{-1/2}]\)
- (b)
\([h^{-1/2}\ c^{1/2}\ G^{1/2}]\)
- (c)
\([h^{1/2}\ c^{-1/2}\ G^{1/2}]\)
- (d)
\([h^{1/2}\ c^{1/2}\ G^{1/2}]\)
Match the physical quantities given in Column I with their dimensions given in Column ll. Select the correct option from the choices given below.
Column I | Column II |
A.Latent heat | 1.\([M^{-1}L^{-2}T^4A^2]\) |
B.Capacitance |
2.\([ML^3T^{-3}A^{-2}]\) |
C.Resistivity | 3.\([M^0L^2T^{-2}]\) |
- (a)
A B C 1 2 3 - (b)
A B C 3 1 2 - (c)
A B C 3 2 1 - (d)
A B C 1 3 2
Dimensions of \({1\over \mu_0\ \varepsilon_0},\) where symbols have their usual meaning, are
- (a)
\([L^{-1}T]\)
- (b)
\([L^{2}T^2]\)
- (c)
\([L^2T^{-2}]\)
- (d)
\([LT^{-1}]\)
The physical quantities not having same dimensions are
- (a)
torque and work
- (b)
momentum and Planck's constant
- (c)
stress and Young's modulus
- (d)
speed and \((\mu_0\varepsilon_0)^{-1/2}\)
Who discovered the principle of inertia?
- (a)
Newton
- (b)
Galileo
- (c)
Tycho Brahe
- (d)
Kepler
Give the nature of work for which Prof. Albert Einstein, a physicist, was awarded the Noble Prize in physics:
- (a)
wave theory of light
- (b)
theory of relativity
- (c)
photoelectric equation
- (d)
wave-particle duality
The unit of energy is:
- (a)
J/s
- (b)
watt-day
- (c)
kilowatt
- (d)
g-cm/s2
Given that y=a cos\(\left( \frac { t }{ p } -qx \right) \) , where t represents time in second and x represents distance in metre. Which of the following statements is true?
- (a)
c
- (b)
The unit of x is same as that of p.
- (c)
The unit of t is same as that of q.
- (d)
The unit of t is same as that of p.
"The weight of a body is 12 g." This statement is not correct because:
- (a)
the weight should be expressed in kg
- (b)
the correct symbol for gram is gm
- (c)
the correct symbol for the unit of weight has not been used.
- (d)
some reason other than those given above
Given that y=A\(\left[ \left( \frac { 2\pi }{ \lambda } \right) (ct-x) \right] \)sin wherey and x are measured in metres. Which of the following statements true?
- (a)
The unit of \(\lambda\) is same as that of x and A.
- (b)
The unit of \(\lambda\) is same as that of x but not of A.
- (c)
The unit of c is same as that of 2\(\frac{\pi}{\lambda}\)
- (d)
The unit of (ct-x) is same as that of 2\(\frac{\pi}{\lambda}\)
The velocity of a particle is given by:
v = at2 + bt + c .
If v is measured in ms -I and t is measured in s, the unit of:
- (a)
a is ms-1
- (b)
b is ms-1
- (c)
c is ms-1
- (d)
a and b are same but that of c is different
Units of magnetic flux are:
- (a)
weber/metre
- (b)
newton x metre/ampere
- (c)
joule x coulomb/metre
- (d)
tesla
SI units of gas constant are:
- (a)
W K -1 mol -1
- (b)
N K-1 mol-1
- (c)
J K-1 mol-1
- (d)
erg K-1 mol-1
Which dimensions will be the same as that of time?
- (a)
[LC]
- (b)
\([\frac{R}{L}]\)
- (c)
\([\frac{L}{R}]\)
- (d)
\([\frac{C}{L}]\)
The velocity v (in em/see) of a particle is given in terms of time t (in see) by the equation: \(\upsilon =at+\frac { b }{ t+c } \) The dimensions of a, band care:
- (a)
a b c [L2] [T] [LT2] - (b)
a b c [LT2] [LT] [L] - (c)
a b c [LT-2] [L] [T] - (d)
a b c [L] [LT] [T2]
A student writes following four different expressions for the displacement 'y' in a periodic motion:
(1) y = a sin \(\frac { 2\pi t }{ T } \)
(2) y = a sin Vt
(3) y = \(\frac { a }{ T } \sin { \frac { t }{ a } } \)
(4) y = \(\frac { a }{ \sqrt { 2 } } \left[ \sin { \frac { 2\pi t }{ T } } +\cos { \frac { 2\pi t }{ T } } \right] \)
where 'a' is maximum displacement, V is the speed and T is the time period; then dimensionally:
- (a)
I and 2 are wrong
- (b)
2 and 3 are wrong
- (c)
3 and 4 are wrong
- (d)
4 and 1 are wrong
A physical quantity depends upon five factors, all of which have dimensions; then method of dimensional analysis:
- (a)
can be applied
- (b)
cannot be applied
- (c)
depends upon factors involved
- (d)
both (a) and (c)
The force F, on a sphere of radius' a' moving in a medium with velocity v is given by: F = 6πηav. The dimensions of η are:
- (a)
[ML-1T-1]
- (b)
[MT-1]
- (c)
[MLT-2]
- (d)
[ML-3]
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 em, 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%
The best method to reduce random errors is:
- (a)
to change the instrument used for measurement
- (b)
to take help of experienced observer
- (c)
to repeat the experiment many times and to take the average results
- (d)
none of the above
A body travels uniformly a distance of (13.8 ± 0.2)m in a time (4.0 ± 0.3)s. The velocity of the body within error limits is:
- (a)
(3.45 ± 0.2) ms-1
- (b)
(3.45 ± 0.3) ms-1
- (c)
(3.45 ± 0.4)ms-1
- (d)
(3.45 ± 0.5) ms-1
A wire has a mass 0.3 ± 0.003 g, radius 0.5 ± 0.005 mm and length 6 ± 0.06 cm, The maximum percentage error in the measurement of density is:
- (a)
1
- (b)
2
- (c)
3
- (d)
4
I ns is defined as:
- (a)
10-9 s of Kr-clock of 1650763.73 oscillations
- (b)
10-9 s of Kr-clock of 652189.63 oscillations
- (c)
10-9 s of Cs-clock of 1650763.73 oscillations
- (d)
10-9 s of Cs-clock of 9192631770 oscillations
The heat dissipated in a resistance can be obtained by the measurement of resistance, the current and time. If the maximum error in the measurement of these quantities is 1%, 2% and 1% respectively, the maximum error in the determination of the dissipated heat is:
- (a)
4%
- (b)
6%
- (c)
\(\frac { 4 }{ 3 } \)%
- (d)
2%
The relative density of a material is found by weighing the body first in air and then in water. If the weight in air is (10.0 ± 0.1)gm and weight in water is (5.0 ± 0.1)gm then the maximum permissible percentage error in relative density is:
- (a)
1%
- (b)
2%
- (c)
3%
- (d)
5%
The minimum number of vectors of unequal magnitude required to produce a zero resultant is:
- (a)
2
- (b)
3
- (c)
4
- (d)
more than 4
Which of the following is not essential for the three vectors to produce zero resultant?
- (a)
The resultant of any two vectors should be equal and opposite to the third vector
- (b)
They should lie in the same plane
- (c)
They should act along the sides of a parallelogram
- (d)
It should be possible to represent them by the three sides of triangle taken in order
What is the projection of \(\overrightarrow { A }\) on \(\overrightarrow { B }\) ?
- (a)
\(\overrightarrow { A } . \overrightarrow { B }\)
- (b)
\(\overrightarrow { A } .\hat { B } \)
- (c)
\(\overrightarrow { B } .\overrightarrow { A } \)
- (d)
\(\hat { A } .\hat { B } \)
Given that \(\overrightarrow { C } =\overrightarrow { A } +\overrightarrow { B } \) and \(\overrightarrow { C }\) makes an angle α with \(\overrightarrow { A }\) and β with \(\overrightarrow { B }\) Which of the following options is correct?
- (a)
α cannot be less than β
- (b)
α < β, if A < B
- (c)
α < β, if A > B
- (d)
α < β, if A = B
The resultant of \(\overrightarrow { A } +\overrightarrow { B } \) is \(\overrightarrow { { R }_{ 1 } } \). On reversing the vector \(\overrightarrow { B }\) the resultant becomes \(\overrightarrow { { R }_{ 2 } } \). What is the value of R21 + R22?
- (a)
A2 + B2
- (b)
A2 - B2
- (c)
2(A2 + B2)
- (d)
2(A2 - B2)
Resultant of two vectors \(\overrightarrow { { F }_{ 1 } } \) and \(\overrightarrow { { F }_{ 2 } } \) is of magnitude P. If \(\overrightarrow { { F }_{ 2 } } \) is reversed, then resultant is of magnitude Q. What is the value of P2 + Q2?
- (a)
F12 +F22
- (b)
F12 - F22
- (c)
2(F12 - F22)
- (d)
2(F12 + F22)
The percentage error in measuring M, Land T are 1%, 1.5% and 3% respectively., Then the percentage error in measuring the physical quantity with dimensions ML-1T-1 is:
- (a)
1%
- (b)
3.5%
- (c)
3%
- (d)
4.5%
- (e)
5.5%
The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 x 10-3 are:
- (a)
5, 1, 2
- (b)
5, 1, 5
- (c)
5, 5, 2
- (d)
4, 4, 2
new system of units is evolved in which the values of \(\mu_{0}\) and £0 are 2 and 8 respectively. Then the speed of light in this system will be
- (a)
0.25
- (b)
0.5
- (c)
0.75
- (d)
1
If vectors \(\hat { i } -3\hat { j } +5\hat { k } \) and \(\hat { i } -3\hat { j } -a\hat { k } \) are equal vectors, then the value of a is :
- (a)
5
- (b)
2
- (c)
-3
- (d)
4
- (e)
-5
Which of the following group have different dimension?
- (a)
Potential difference, emf, voltage
- (b)
Pressure, stress, Young's modulus
- (c)
Heat, energy, work done
- (d)
Dipole moment, electric flux, electric field
If the angle between the vector\(\vec{A}\) and \(\vec{B}\) is \(\theta\), the value of the product (\(\vec{B}\) x \(\vec{A}\) ).\(\vec{A}\) is equal to:
- (a)
BA2 cos \(\theta\)
- (b)
BA2 sin \(\theta\)
- (c)
BA2 sin \(\theta\)cos\(\theta\)
- (d)
zero
The dimensions of permittivity £0 are:
- (a)
[M-1L-3 A 2T4]
- (b)
[M-1L 3A -2T-4]
- (c)
[M-1L-1A2T2]
- (d)
[M-1L-3A2T-4]
Dimensional formula of intensity of radiation is:
- (a)
[M1L2T-2]
- (b)
[M1L0T3]
- (c)
[M1L0T-3]
- (d)
[M0L2T-2]
Which two of the following five physical parameters have the same dimensions?
1. Energy density
2. Refractive index
3. Dielectric constant
4. Young's modulus
5. Magnetic field
- (a)
1 and 4
- (b)
1 and 5
- (c)
2 and 4
- (d)
3 and 5
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 = 0.1 s.
Student | Length of the pendulum (cm) | Number of oscillations (n) | Total time (s) for oscillations (n) | Time period (s) |
---|---|---|---|---|
I | 64.0 | 8 | 128.0 | 16.0 |
II | 64.0 | 4 | 64.0 | 16.0 |
III | 20.0 | 4 | 36.0 | 9.0 |
If E1, EII and EIII are the percentage errors in g
i.e., (\(\frac { \Delta g }{ g } \) \(\times\) 100) for students I, II and III respectively,
- (a)
E1=0
- (b)
E1 is minimum
- (c)
E1 = E11
- (d)
E11 is maximum
\(\vec { A } \)and\(\vec {B } \) are two vectors given by\(\vec { A } =2\hat { i } +3\hat { j } \) and\(\vec { B } =\hat { i } \hat { j } .\) The magnitude of the component of\(\vec { A }\) along \(\vec { B }\)is
- (a)
\(\frac { 5 }{ \sqrt { 2 } } \)
- (b)
\(\frac { 3 }{ \sqrt { 2 } } \)
- (c)
\(\frac { 7 }{ \sqrt { 2 } } \)
- (d)
\(\frac {1 }{ \sqrt { 2 } } \)
Which of the following sets of quantities have same dimensional formulae?
- (a)
Frequency, angular frequency and angular momentum
- (b)
Surface tension, stress and spring constant
- (c)
Acceleration, momentum and retardation
- (d)
Thermal capacity, specific heat and entropy
- (e)
Work, energy and torque
Consider three vectors \(\overrightarrow { A } =\hat { i } +\hat { j } -2\hat { k } ,\overrightarrow { B } =\hat { i } -\hat { j } +\hat { k } \) and \(\overrightarrow { C } =2\hat { i } -3\hat { j } +4\hat { k } \) . A vector \(\overrightarrow { X } \) of the form \(\alpha \overrightarrow { A } +\beta \overrightarrow { B } \) (\(\alpha\) and \(\beta\) are numbers) is perpendicular to \(\overrightarrow { C } \) . The ratio of \(\alpha\) and \(\beta\) is:
- (a)
1 : 1
- (b)
2 : 1
- (c)
-1 : 1
- (d)
3 : 1