Physics - Units and measurement
Exam Duration: 45 Mins Total Questions : 30
The dimensions of Planck's constant are equal to that of
- (a)
linear momentum
- (b)
angular velocity
- (c)
angular momentum
- (d)
energy
The dimension of \(\frac { { e }^{ 2 } }{ { t }_{ 0 }hc } \) are
- (a)
[M-1 L-3T4 A2]
- (b)
[ML3T4 A-2]
- (c)
[M0L0T0 A0]
- (d)
[M-1 L-3 T2 A]
Which of the following has metre-kelvin as the unit?
- (a)
Rydberg constant
- (b)
Wien's constant
- (c)
Solar constant
- (d)
Gas constant
Dimension of impulse are
- (a)
\([ML^{-2}T^{-3}]\)
- (b)
\([ML^{-2}]\)
- (c)
\([MLT^{-1}]\)
- (d)
\([MLT^{-2}]\)
Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon the velocity v of the water, its density \(\rho\) and the acceleration due to gravity g. Then, m is directly proportional to
- (a)
\(v^2\)
- (b)
\(v^4\)
- (c)
\(v^5\)
- (d)
\(v^6\)
In the formula, \(X=3Y\ Z^2, X\) and Z have dimensions of capacitance and magnetic induction. The dimensions of Y in MKS system are
- (a)
\([M^{-3}L^{-2}T^{8}Q^{4}]\)
- (b)
\([ML^2T^8Q^4]\)
- (c)
\([M^{-2}L^{-3}T^{2}Q^{4}]\)
- (d)
\([M^{-2}L^{-2}TQ^{2}]\)
The length, width and thickness of a block are \(({100.0\ ^+_-\ 0.1})cm, (10.00\ ^+_-\ 0.001)cm\) respectively. The most probable error in its volume wil be
- (a)
\(^+_-\ 0.111\ cm^3\)
- (b)
\(^+_-\ 0.012\ cm^3\)
- (c)
\(^+_-\ 0.03\ cm^3\)
- (d)
None of these
Which of the following units denotes the dimensions \([ML^2/Q^2], \) where Q denotes the electric charge?
- (a)
\(WB/m^2\)
- (b)
Henry (H)
- (c)
\(H/m^2\)
- (d)
\(Weber\ (Wb)\)
Einstein's name is associated with the discovery of:
- (a)
nuclear model of atom
- (b)
neutron
- (c)
theory of relativity
- (d)
expansion of the universe
Two India born American scientist who were awarded Noble Price are :
- (a)
S. Bose and Narlikar
- (b)
E.C.G. Sudarshan and Bhagwantam
- (c)
C.V. Raman and H.J. Bhabha
- (d)
S. Chandrashekhar and A. Salam
The dimensional formula for angular momentum is:
- (a)
[ML2T-2]
- (b)
[ML2T-1]
- (c)
[MLT-1]
- (d)
[M0L2T-2]
In the relation: y = a cos (ωt + Kx), the dimensional formula for Kx is same as that of:
- (a)
a/ω
- (b)
a/y
- (c)
ωt/a
- (d)
ya/ ωt
Dimensional analysis can be used to derive formulae:
- (a)
containing trigonometrical functions
- (b)
containing exponential functions
- (c)
containing logarithmic functions
- (d)
none of the above
A student writes the escape velocity as: \({ \upsilon }_{ e }=\sqrt { \frac { GM }{ { R }^{ 2 } } } \) The equation is:
- (a)
dimensionally incorrect
- (b)
dimensionally correct
- (c)
numerically correct
- (d)
both (a) and (c)
Which of the following have same dimensions?
- (a)
Pressure and density
- (b)
Gravitational potential and energy
- (c)
Impulse and momentum
- (d)
Stress and strain
The velocity of water waves may depend on their wavelength A , the density of water p and the acceleration due to gravity g. The method of dimensional analysis gives the following relation between these quantities:
- (a)
v2 = Kλ-1g-1p-1
- (b)
v2 = Kλg
- (c)
v2 =Kλpg
- (d)
v2 = Kλ3g-1p-1
The radius of a ball is (5.2 ± 0.2)cm. The percentage error in the volume of the ball is.
- (a)
11%
- (b)
4%
- (c)
7%
- (d)
9%
The length of one rod is 2.53 cm and that of the other is 1.27 cm. The least count of measuring instrument is 0.01 cm. If two rods are put together end to end, the combined length can be expressed as:
- (a)
(3.80 ± 0.01)cm
- (b)
(3.80 ± 0.02)cm
- (c)
(3.80 ± 0.03)cm
- (d)
(3.80 ± 0.04) cm
If physical quantity X is represented by X = MaLbT-c and the maximum percentage errors in M, L and T are α%, β% and ⋎ % respectively, then the total maximum percentage error in X is:
- (a)
(αa + βb - ⋎c)%
- (b)
(αa + βb + ⋎c)%
- (c)
(αa - βb - ⋎c)%
- (d)
none of these
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
At what angle the two vectors of magnitudes (A + B) and (A - B) must act, so that the resultant is \(\sqrt { { A }^{ 2 }+{ B }^{ 2 } } \)?
- (a)
cos-1 \(\frac { { A }^{ 2 }-{ B }^{ 2 } }{ { A }^{ 2 }+{ B }^{ 2 } } \)
- (b)
cos-1 \(\frac { { A }^{ 2 }+{ B }^{ 2 } }{ { B }^{ 2 }-{ A }^{ 2 } } \)
- (c)
cos-1 \(\frac { { A }^{ 2 }-{ B }^{ 2 } }{ 2\left( { A }^{ 2 }+{ B }^{ 2 } \right) } \)
- (d)
cos-1 \(\frac { { A }^{ 2 }+{ B }^{ 2 } }{ 2\left( { B }^{ 2 }-{ A }^{ 2 } \right) } \)
hat is the angle between \(\overrightarrow { A } +\overrightarrow { B } \) and \(\overrightarrow { A } \times \overrightarrow { B } \) ?
- (a)
0
- (b)
π/4
- (c)
π/2
- (d)
π
The direction of \(\vec { A } \) is vertically upward and direction of \(\vec { B } \) is in north direction. The direction of \(\vec { A } \times \vec { B } \) will be:
- (a)
western direction
- (b)
eastern direction
- (c)
at 45° upward in north
- (d)
vertically downward
Angle between \(\overrightarrow { P }\) and \(\overrightarrow { Q }\) is θ. What is the value of \(\overrightarrow { P } .\overrightarrow { Q } \times \overrightarrow { P } \)?
- (a)
P2Q cosθ
- (b)
Zero
- (c)
p2Q sinθcosθ
- (d)
p2Q sinθ
Surface tension has the same dimensions as that of:
- (a)
coefficient of viscosity
- (b)
impulse
- (c)
momentum
- (d)
spring constant
- (e)
frequency
Which of the following is not a vector quantity?
- (a)
Momentum
- (b)
Weight
- (c)
Potential energy
- (d)
Nuclear spin
If E = energy, G = gravitational constant, I = impulse and M = mass, the dimensions of GIM2 IE2 are same as that of:
- (a)
time
- (b)
mass
- (c)
length
- (d)
force
Given \(\vec { C } =\vec { A } \times \vec { B } \)and\(\vec { D} =\vec {B } \times \vec { A } \) . What is the angle between \(\vec { C } \) and \(\vec { D } \)?
- (a)
30o
- (b)
60o
- (c)
90o
- (d)
180o