IISER Physics - Units and measurement
Exam Duration: 45 Mins Total Questions : 30
A small sphere of radius r with a velocity v under streamline conditions in a viscous fluid experiences a retarding force F given by \(F=Kr\vartheta \) where K is a dimensonless constant. The SI system have the dimensions in mass, length and time as
- (a)
1, -2, -2
- (b)
1, -1, +1
- (c)
1, -1, -1
- (d)
1, 1, -2
Angular velocity is
- (a)
A scalar
- (b)
an axial vector
- (c)
a polar vector
- (d)
a tensor
The dimension of light are
- (a)
[L]
- (b)
[T]
- (c)
[M0L0T0]
- (d)
[ML2T-2]
A force F is given by F = at + bt2, where t is time. What are the dimensions of a and b?
- (a)
[M1L1T-3] and [M1L1T4]
- (b)
[MLT-3] and [MLT4]
- (c)
[MLT-1] and [MLT0]
- (d)
[MLT-4] and [MLT-1]
Joule.second is the unit of
- (a)
energy
- (b)
momentum
- (c)
angular momentum
- (d)
power
The number of particles is given by \(n=-Q{n_2-n_1\over x_2-x_1}.\) Crossing a unit area perpendicular \(n_1\) and \(n_2\) are number of particles per unit volume for \(x_2\) and \(x_1\). Find dimension of Q, (called diffusion constant).
- (a)
\([M^0LT^2]\)
- (b)
\([M^0L^2T^{-4}]\)
- (c)
\([M^0LT^{-3}]\)
- (d)
\([M^0L^2T^{-1}]\)
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
A body of mass \(m=3.513\ kg\) is moving along the x-axis with a speed of \(5.00\ ms^{-1}.\) The magnitude of its momentum is recorded as
- (a)
17.6 \(kg-ms^{-1}\)
- (b)
17.565 \(kg-ms^{-1}\)
- (c)
17.56 \(kg-ms^{-1}\)
- (d)
17.57 \(kg-ms^{-1}\)
Which of the following is the name of a physical quantity?
- (a)
Parsec
- (b)
Fermi
- (c)
Energy
- (d)
Light-year.
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.
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 length of a strip measured with a metre rod is 10.0 cm. Its width measured with a Vernier callipers is 1.00 cm. The least count of the metre rod is 0.1 cm and that of Vernier callipers 0.01 cm. What will be error in its area?
- (a)
± 0.01cm2
- (b)
±0.1 cm2
- (c)
± 0.11 cm2
- (d)
± 0.2 cm2
The random error in the arithmetic mean of 100 observations is x, then random error in the arithmetic mean
of 400 observations would be:
- (a)
4x
- (b)
\(\frac { 1 }{ 4 } x\)
- (c)
2x
- (d)
\(\frac { 1 }{ 2 } x\)
Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is:
- (a)
1%
- (b)
3%
- (c)
5%
- (d)
7%
The vectors \(\overrightarrow { A } \) and \(\overrightarrow { B } \) are such that \(\left| \overrightarrow { A } +\overrightarrow { B } \right| =\left| \overrightarrow { A } -\overrightarrow { B } \right| \) then the angle between the two vectors \(\overrightarrow { A } \) and \(\overrightarrow { B } \) will be:
- (a)
0°
- (b)
60°
- (c)
90°
- (d)
1800
Two vectors \(\overrightarrow { A } \) and \(\overrightarrow { B } \) are such that \(\overrightarrow { A } +\overrightarrow { B } =\overrightarrow { C } \) and A2 + B2 = C2. If θ is the angle between positive directions of \(\overrightarrow { A } \) and \(\overrightarrow { B } \) then mark the correct alternative:
- (a)
θ = 00
- (b)
θ = \(\frac { \pi }{ 2 } \)
- (c)
θ = \(\frac { 2\pi }{ 3 } \)
- (d)
θ = π
What is the angle between \(\overrightarrow { A } \times \overrightarrow { B } \) and \(\overrightarrow { B } \times \overrightarrow { A } \) ?
- (a)
Zero
- (b)
π/4
- (c)
π/2
- (d)
None of these
The mass and volume of a body are found to be 5.00 ± 0.05 kg and 1.00 ± 0.05m3 respectively. Then the maximum possible percentage error in its density is:
- (a)
6%
- (b)
3%
- (c)
10%
- (d)
5%
- (e)
7%
Consider the following equation of Bemoulli's theorem: P + \(\frac { 1 }{ 2 } \rho { \upsilon }^{ 2 }\) + ρgh = K (constant). The dimensions of K/P are same as which of the following?
- (a)
Thrust
- (b)
Pressure
- (c)
Angle
- (d)
Viscosity
If voltage V = (100 ± 5) V and current! = (10 ± 0.2) A, the percentage error in resistance R is:
- (a)
5.2%
- (b)
25%
- (c)
7%
- (d)
10%
- (e)
2.5%
If the units of mass, length and time are doubled, unit of angular momentum will be:
- (a)
doubled
- (b)
tripled
- (c)
quadrupled
- (d)
8 times the original value
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
A and B are two vectors and θ is the angle between them, if \(\left| \overrightarrow { A } \times \overrightarrow { B } \right| =\sqrt { 3 } \left( \overrightarrow { A } .\overrightarrow { B } \right) \) the value of θ is:
- (a)
45°
- (b)
30°
- (c)
90°
- (d)
60°
A student performs an experiment for determination of g (= 4π2I/T2 ), I = 1m and he commits an error of Δl.For T, he takes the time of n oscillations with the stop-watch of least count ΔT and he commits a human error of 0.1 sec. For which of the following data, the measurement of g will be most accurate?
- (a)
Δl ΔT n amplitude of
oscillation5 mm 0.2 sec 10 5 mm - (b)
Δl ΔT n amplitude of
oscillation5 mm 0.2 sec 20 5 mm - (c)
Δl ΔT n amplitude of
oscillation5 mm 0.1 sec 20 1 mm - (d)
Δl ΔT n amplitude of
oscillation5 mm 0.1 sec 50 1 mm
If force is proportional to square of velocity, then the dimensions of proportionality constant is:
- (a)
[ML-1T]
- (b)
[ML-1T0]
- (c)
[MLT0]
- (d)
[M0LT-1]
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
The square of resultant of two equal forces is three times their product. Angle between the forces is:
- (a)
\(\pi\)
- (b)
\(\frac { \pi }{ 2 } \)
- (c)
\(\frac { \pi }{ 4 } \)
- (d)
\(\frac { \pi }{ 3 } \)
If \(\vec{A}\) = 2\(\hat{i}\) + 3\(\hat{j}\) - \(\hat{k}\) and B = - i + 3\(\hat{j}\) + 4\(\hat{k}\), then projection of \(\vec{A}\) and \(\vec{B}\) on 11 will be:
- (a)
\(\frac{3}{\sqrt{13}}\)
- (b)
\(\frac{3}{\sqrt{26}}\)
- (c)
\(\sqrt{\frac{3}{26}}\)
- (d)
\(\sqrt{\frac{3}{13}}\)
\(\vec { A } \)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)
\(\frac {1 }{ \sqrt { 2 } } \)
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