JEE Main Physics - Units and Measurement
Exam Duration: 60 Mins Total Questions : 30
The SI unit of Gravitational field indensity is
- (a)
ms-2
- (b)
J kg-1
- (c)
N kg m-2
- (d)
kg N-1
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 one of the following represent the correct dimensions of the coefficient of viscosity?
- (a)
\([ML^{-1}]T^{-2}\)
- (b)
\([MLT^{-1}]\)
- (c)
\([ML^{-1}T^{-1}]\)
- (d)
\([ML^{-2}T^{-2}]\)
Two current areas in which physics and technology are closely interlinked are:
- (a)
rocket propulsion and launching of satellites
- (b)
nuclear fission and nuclear fusion
- (c)
lasers and microelectronics
- (d)
none of the above
In superconductivity there is production of:
- (a)
low magnetic field
- (b)
medium magnetic fields
- (c)
ultra high magnetic fields
- (d)
none of these
The unit of Stefan-Boltzmann's constant (σ) is:
- (a)
\(\frac { { watt }^{ 4 } }{ m\times { K }^{ 4 } } \)
- (b)
\(\frac { calorie }{ { m }^{ 2 }\times { K }^{ 4 } } \)
- (c)
\(\frac { watt }{ { m }^{ 2 }\times { K }^{ 4 } } \)
- (d)
\(\frac { joule }{ { m }^{ 2 }\times { K }^{ 4 } } \)
kWh is a unit of:
- (a)
power
- (b)
energy
- (c)
force
- (d)
temperature
The dimensional representation oflatent heat is identical to that of:
- (a)
internal energy
- (b)
angular momentum
- (c)
gravitational potential
- (d)
electric potential
The dimensional formula for impulse is:
- (a)
[MLT-1]
- (b)
[ML2T-1]
- (c)
[ML2T2]
- (d)
[ML0T2]
If we choose velocity V, acceleration A and force F as the fundamental quantities, then the angular momentum in terms of V, A and F would be:
- (a)
[FA-1V]
- (b)
[FV3 A-2]
- (c)
[FV2 A-1]
- (d)
[ML2T1]
If V = \(\sqrt { \frac { \gamma P }{ \rho } } \) then dimensions of \(\gamma\) are:
- (a)
[M0L0T0]
- (b)
[M0L0T-1]
- (c)
[M1L0T0]
- (d)
[MoL1T0]
If the acceleration due to gravity is 10ms-2 and the units of length and time are changed to kilometre and hour, respectively, the numerical value of the acceleration is:
- (a)
360000
- (b)
72000
- (c)
36000
- (d)
129600
The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimate of the kinetic energy obtained by measuring mass and speed?
- (a)
11%
- (b)
8%
- (c)
5%
- (d)
1%
If Q = \(\frac { { X }^{ n } }{ { Y }^{ m } } \) and ΔX is absolute error in the measurement of X, ΔY is absolute error in the measurement of Y, then absolute error ΔQ in Q is:
- (a)
\(\Delta Q=\pm \left( n\frac { \Delta X }{ X } +m\frac { \Delta Y }{ Y } \right) \)
- (b)
\(\Delta Q=\pm \left( n\frac { \Delta X }{ X } +m\frac { \Delta Y }{ Y } \right) Q\)
- (c)
\(\Delta Q=\pm \left( n\frac { \Delta X }{ X } -m\frac { \Delta Y }{ Y } \right) Q\)
- (d)
\(\Delta Q=\pm \left( n\frac { \Delta X }{ Y } -m\frac { \Delta Y }{ X } \right) Q\)
While measuring acceleration due to gravity by a simple pendulum, a student makes a positive error of 2% in the length of the pendulum and a positive error of 1% in the value of time period. His actual percentage error in the measurement of the value of g will be:
- (a)
3%
- (b)
0%
- (c)
4%
- (d)
5%
The length and breadth of a metal sheet are 3.124 m and 3.002 m respectively. The area of this sheet upto four correct significant figures is:
- (a)
9.37 m2
- (b)
9.378 m2
- (c)
9.3782 m2
- (d)
9.378248 m2
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
What is the maximum number of rectangular components into which a vector can be split in its own plane?
- (a)
2
- (b)
3
- (c)
4
- (d)
Infinite
If a unit vector is represented by \(0.5\hat { i } +0.8\hat { j } +c\hat { k } \) then the value of 'c' is:
- (a)
0
- (b)
\(\sqrt { 0.11 } \)
- (c)
\(\sqrt { 0.01 } \)
- (d)
\(\sqrt { 0.39 } \)
If \(\overrightarrow { A } +\overrightarrow { B } =\overrightarrow { C } \) and A = B = C then what should be the angle between \(\overrightarrow { A } \) and \(\overrightarrow { B } \) ?
- (a)
0
- (b)
π/3
- (c)
2π/3
- (d)
π
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
A physical quantity Q is found to depend on observables x, y and z, obeying relation Q=\(\frac { x^{ 3 }{ y }^{ 2 } }{ z } \) . The percentage error in the measurements of x, y and Z are 1%, 2% and 4% respectively. What is percentage error in the quantity Q?
- (a)
11%
- (b)
4%
- (c)
1%
- (d)
3%
Dimensions of electrical resistance is:
- (a)
[ML2T-3A-1]
- (b)
[ML2T-3A-2]
- (c)
[ML3T-3A-2]
- (d)
[ML-1T3 A2]
The sum of two vectors \(\vec{A}\) and \(\vec{B}\) is at right angles to their difference. Then
- (a)
A= B
- (b)
A = 2B
- (c)
B = 2A
- (d)
\(\vec{A}\) and \(\vec{B}\) have the same direction
The energy (E ), angular momentum (L) and universal gravitational constant (G) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant (h) is
- (a)
0
- (b)
-1
- (c)
\(\frac { 5 }{ 3 } \)
- (d)
1
The magnetic moment has dimensions of:
- (a)
[LA]
- (b)
[L2A]
- (c)
[LT-1A]
- (d)
[L2T-1A]
If the unit of force is I kilo newton, the length is I km and time 100 s, what will be the unit of mass?
- (a)
1,000 kg
- (b)
1 Kg
- (c)
10,000 Kg
- (d)
100 Kg
Two vectors are perpendicular, if:
- (a)
\(\vec{A}.\vec{B}\)=1
- (b)
\(\vec{A}\times\vec{B}\)=0
- (c)
\(\vec{A}.\vec{B}\)=0
- (d)
\(\vec{A}\times\vec{B}\)=AB
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