Physics - Units and Measurement
Exam Duration: 45 Mins Total Questions : 30
Dimension of compressibility of a substance is
- (a)
+2 in time
- (b)
+1 in mass
- (c)
-1 in length
- (d)
-2 in time
Dimensions of action are
- (a)
MLT-1
- (b)
ML2T-1
- (c)
ML2T-2
- (d)
ML2T-3
Which of the following quantities can be written in SI units in kg m2 A-2 s-3 ?
- (a)
Resistance
- (b)
Inductance
- (c)
Capacitance
- (d)
Magnetic flux
A force F is applied on a square plate of size L. If the percentage error in determination of L is 2% and that in F is 4%, the permissible error in pressure is
- (a)
2%
- (b)
4%
- (c)
6%
- (d)
8%
Joule-secondis the SI unit of
- (a)
Eistein's constant
- (b)
Boltzmann's constant
- (c)
Planck's constant
- (d)
Loschmidt's constant
Suppose the torque acting on a body is given by \(\tau=KL+(MI/\omega)\), where L=angular momentum, I= moment of inertia and \(\omega\) = angular speed. The dimensional formula for KM is same as that for
- (a)
\(time^{-4}\)
- (b)
\(time^{-2}\)
- (c)
\(time^{2}\)
- (d)
\(time^{4}\)
Let \([\varepsilon _0]\) denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then
- (a)
\([\varepsilon _0]=[M^{-1}L^{-3}T^2A]\)
- (b)
\([\varepsilon _0]=[M^{-1}L^{-3}T^2A]\)
- (c)
\([\varepsilon _0]=[M^{-1}L^{-3}T^2A]\)
- (d)
\([\varepsilon _0]=[M^{-1}L^{-3}T^2A]\)
In an experiment, the angles are required to be measured using an instrument. 29 division of the main scale exactly coincide with the 30 division of the main scale is half-a-degree \((=0.5^o)\), then the least count of the = instrument is
- (a)
one minute
- (b)
half minute
- (c)
one degree
- (d)
half degree
Who invented wireless telegraphy?
- (a)
Maxwell
- (b)
Marconi
- (c)
Hertz
- (d)
Faraday
Who was awarded Nobel Prize for the theory of the unification of weak and electromagnetic interaction?
- (a)
Rutherford
- (b)
A. Salam
- (c)
H.J. Bhabha
- (d)
S. Chandrashekar
In superconductivity there is production of:
- (a)
low magnetic field
- (b)
medium magnetic fields
- (c)
ultra high magnetic fields
- (d)
none of these
The number of particles crossing the unit area perpendicular to the x-axis per unit time is given by: N =-D where n1 and n2 are the numbers of particles per unit volume for the values of x meant to be x1 and x2 respectively. What is the dimensional formula for the diffusion constant D?
- (a)
[M0LT2]
- (b)
[M0L2T4]
- (c)
[M0LT-3]
- (d)
[M0L2T-1]
The dimensional formula for bulk modulus of elasticity is:
- (a)
[M1 L-2T2]
- (b)
[M1L-3T-2]
- (c)
[M1L2T-2]
- (d)
[M1L-1T-2]
If ε0 , μ0 and c represent the relative permittivity of free space, the magnetic permeability of free space and the velocity of light respectively, which of the following combinations is correct?
- (a)
\(c=\frac { 1 }{ { \mu }_{ 0 }\varepsilon _{ 0 } } \)
- (b)
\(c=\frac { 1 }{ \sqrt { { \mu }_{ 0 }\varepsilon _{ 0 } } } \)
- (c)
c = μ0ε0
- (d)
\(c=\sqrt { { \mu }_{ 0 }\varepsilon _{ 0 } } \)
If area (A), velocity (v) and density (p) are taken as fundamental units, what is the dimensional formula for force?
- (a)
[Av2ρ]
- (b)
[A2vρ]
- (c)
[Avρ2]
- (d)
[Avρ]
Height of liquid in a capillary tube is given as: h=2Scosθ/rpg. Where S is the surface tension of liquid, r is the radius of capillary tube, p is density and g is acceleration due to gravity then dimensional formula for S is:
- (a)
[ML0T-2]
- (b)
[MoLT-2]
- (c)
[ML2T-2]
- (d)
[M0L0T-3]
Given that the amplitude A of scattered light is:
(i) directly proportional to the amplitude (λ0) of incident light.
(ii) directly proportional to the volume (V)ofthe scattering particle.
(iii) inversely proportional to the distance (r) from the scattered particle.
(iv) depend upon the wavelength (λ)ofthe scattered light.
Then:
- (a)
\(A\propto \frac { 1 }{ \lambda } \)
- (b)
\(A\propto \frac { 1 }{ { \lambda }^{ 2 } } \)
- (c)
\(A\propto \frac { 1 }{ { \lambda }^{ 3 } } \)
- (d)
\(A\propto \frac { 1 }{ { \lambda }^{ 4 } } \)
While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation g = 4π2 (l/T2) will be:
- (a)
2%
- (b)
4%
- (c)
7%
- (d)
10%
A student performs experiment with simple pendulum and measures time for 10 vibrations. Ifhe measures the time for 100 vibrations, the error in the measurement of time period will be reduced by a factor of:
- (a)
10
- (b)
90
- (c)
100
- (d)
1000
The two vectors have magnitudes 3 and 5. If angle between them is 60°, then the dot product of two vectors will be:
- (a)
7.5
- (b)
6.5
- (c)
8.4
- (d)
7.9
Which of the following operations make no sense in case of scalars and vectors?
- (a)
Multiplying any vector by a scalar
- (b)
Adding a component of vector to the same vector
- (c)
Multiplying any two scalars
- (d)
Adding a scalar to a vector of the same dimensions
Angular momentum is:
- (a)
axial vector
- (b)
polar vector
- (c)
scalar
- (d)
none of these
If \(\left| \overrightarrow { P } \right| =\left| \overrightarrow { Q } \right| \) and the angle between \(\overrightarrow { P } \) and \(\overrightarrow { Q } \) is neither 0° nor 180°, then what is the angle between \(\overrightarrow { P } +\overrightarrow { Q } \) and \(\overrightarrow { P } -\overrightarrow { Q } \)?
- (a)
0°
- (b)
30°
- (c)
60°
- (d)
90°
The dimension of magnetic field in M, L, T and C (Coulomb) is given as:
- (a)
[MLT-1C-1]
- (b)
[MT2C-2]
- (c)
[MT-1C-1]
- (d)
[MT-2C-1]
If |\(\vec{A}\) x \(\vec{B}\) |= \(\sqrt{3}\)\(\vec{A}\) .\(\vec{B}\), then the value of | \(\vec{A}\) + \(\vec{B}\)| is:
- (a)
(A2 +B2 +AB)1/2
- (b)
\(\left( { A }^{ 2 }+{ B }^{ 2 }+{ \frac { AB }{ \sqrt { 3 } } } \right) ^{ 1/2 }\)
- (c)
(A+B)
- (d)
(A2+B2+\(\sqrt{3}\)AB)1/2
Given that the displacement of an oscillating particle is given by y = A sin(Bx + Ct + D). The dimensional formula for ABCD is
- (a)
[M0L-1T0]
- (b)
[M0L0T-1]
- (c)
[M0L-1T-1]
- (d)
[M0L0T0]
The dimensions of \(\frac { { e }^{ 2 } }{ 4\pi { \varepsilon }_{ 0 }hc } \)where e, £0, hand care electronic charge, electric permittivity, Planck's constant electronic charge, electric permittivity, Planck's constant
- (a)
M0L0T0]
- (b)
[ML0T0]
- (c)
[M0LT0]
- (d)
[M0L0T]
If the two vectors \(\overrightarrow { A } =2\hat { i } +3\hat { j } +4\hat { k } \) and \(\overrightarrow { B } =\hat { i } +2\hat { j } -n\hat { k } \) are perpendicular, then the value of n is:
- (a)
1
- (b)
2
- (c)
3
- (d)
4
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
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