Physics - Units and Measurement Question Paper 1
Exam Duration: 45 Mins Total Questions : 30
A highly rigid cubical block A of small mass M and side L is fixed rigidly on to another cubical block of same dimensions and of low modulus of rigidity \(\eta \), such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn, block A executes small oscillations, the time period of which is given by
- (a)
\(2\pi \sqrt { M \eta L } \)
- (b)
\(2\pi \sqrt { \frac { M \eta }{ L } } \)
- (c)
\(2\pi \sqrt { \frac { M L }{ \eta} } \)
- (d)
\(2\pi \sqrt { \frac { M }{ \eta L } } \)
The dimensions of \(h\over e\) are same as that of
- (a)
magnetic field induction
- (b)
magnetic flux
- (c)
electric field strength
- (d)
electric flux
A quantity X is given by \({ \epsilon }_{ 0 }L\frac { \triangle V }{ \triangle t } \) where \({ \epsilon }_{ 0 }\) is the permittivity of free space, L is a length, \(\triangle V\) is a potential difference and \(\triangle t\) is a time interval. The dimensional formula for X is the same as that of
- (a)
resistance
- (b)
charge
- (c)
voltage
- (d)
current
Which of the following will have the dimensions of time?
- (a)
LC
- (b)
\(R\over L\)
- (c)
\(L\over R\)
- (d)
\(C\over L\)
If force (f), acceleration (a) and time (T) are used as the fundamental units, the dimensional formula for length will be
- (a)
\([F^0aT^2]\)
- (b)
\([Fa^0T^2]\)
- (c)
\([Fa^2T^0]\)
- (d)
\([FaT]\)
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
Who discovered the principle of inertia?
- (a)
Newton
- (b)
Galileo
- (c)
Tycho Brahe
- (d)
Kepler
The ratio of the SI unit to the CGS unit of modulus of rigidity is:
- (a)
102
- (b)
10-2
- (c)
10-1
- (d)
10
Why is it wrong to express 106 km as Mkm?
- (a)
M is not the symbol for 106
- (b)
Use of double prefixes is conventionally prohibited
- (c)
Symbols for the units other than commemorating great scientist are not written as capital letters.
- (d)
Because of some reason other than those mentioned above
Which of the following units is used to measure the radius of nucleus?
- (a)
Micron
- (b)
Nanometer
- (c)
Angstrom
- (d)
Femtometer
If C and R denote capacity and resistance respectively, the dimensions of CR are:
- (a)
[M0L0T1]
- (b)
`[M0L2T -2]
- (c)
[M0L0T-2]
- (d)
[ML0T0]
The dimension of the ratio of angular to linear momentum is:
- (a)
[M0LT0]
- (b)
[MLT-1]
- (c)
[ML2T-1]
- (d)
[M-1L-1T-1]
With usual notation, amongst the following, the one which does not represent the dimensions of time is:
- (a)
\(\left[ \frac { L }{ R } \right] \)
- (b)
[RC]
- (c)
\(\left[ \sqrt { LC } \right] \)
- (d)
\(\left[ \frac { 1 }{ \sqrt { LC } } \right] \)
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
If energy (E), velocity (v) and force (F) be taken as fundamental quantities, then what are the dimensions of mass?
- (a)
[Ev2]
- (b)
[Ev-2]
- (c)
[Fv-1]
- (d)
[Fv-2]
The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to minimum force, then the forces are:
- (a)
6 N and 10 N
- (b)
8 N and 8 N
- (c)
4 N and 12 N
- (d)
2 N and 14 N
Component of \(3\hat { i } +4\hat { j } \) perpendicular to \(\hat { i } +\hat { j } \) and in the same plane as that of \(3\hat { i } +4\hat { j } \) is:
- (a)
\(\frac { 1 }{ 2 } \left( \hat { j } -\hat { i } \right) \)
- (b)
\(\frac { 3 }{ 2 } \left( \hat { j } -\hat { i } \right) \)
- (c)
\(\frac { 5 }{ 2 } \left( \hat { j } -\hat { i } \right) \)
- (d)
\(\frac { 7 }{ 2 } \left( \hat { j } -\hat { i } \right) \)
A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction:
- (a)
due north
- (b)
30° east of north
- (c)
30° west of north
- (d)
60° east of north
The SI unit of electron mobility is:
- (a)
m2s-1V-1
- (b)
msV-1
- (c)
ms-1V
- (d)
m2s-2V-2
Given that A = B. What is the angle between \(\overrightarrow { A } +\overrightarrow { B } \) and \(\overrightarrow { A } -\overrightarrow { B } \)?
- (a)
30°
- (b)
60°
- (c)
90°
- (d)
180°
A body of mass 2 kg is constrained to move along the Y-direction. When a force of 2\(\hat { i }\) + 5\(\hat { j }\) + 7\(\hat { k }\) newton acts on it and the body is displaced through 10m, the kinetic energy gained by the body is:
- (a)
50 J
- (b)
100 J
- (c)
150 J
- (d)
350 J
The unit of electric field is not equivalent to:
- (a)
\(\frac{J}{C}\)
- (b)
\(\frac{J}{Cm}\)
- (c)
\(\frac{V}{m}\)
- (d)
\(\frac{N}{C}\)
Which ofthe following is the smallest unit?
- (a)
Millimetre
- (b)
Angstrom
- (c)
Fermi
- (d)
Metre
If the vectors \(\overrightarrow { P } =a\hat { i } +a\hat { j } +3\hat { k } \) and \(\overrightarrow { Q } =a\hat { i } -2\hat { j } -\hat { k } \) perpendicular to each other, then the positive value of a is:
- (a)
3
- (b)
2
- (c)
1
- (d)
0
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
A particle is moving in a circle of radius 'r' with a constant speed '\(\upsilon\)'. The change in velocity after the particle has travelled a distance equal to (1/8) of the circumference of the circle is:
- (a)
0.125 \(\upsilon\)
- (b)
0.500 \(\upsilon\)
- (c)
0.765 \(\upsilon\)
- (d)
zero
The position of the particle moving along y -axis is given as: y = At2 - Bt3 , where y is measured in metre and t in second. Then the dimensions of B is:
- (a)
[LT2]
- (b)
[LT-1]
- (c)
[LT-3]
- (d)
[MLT-2]
The angle between the vectors \(\left( \hat { i } +\hat { j } \right) \) and \(\left( \hat { j } +\hat { k } \right) \) is:
- (a)
90°
- (b)
60°
- (c)
30°
- (d)
45°
A particle has the position vector \(\vec{r}\)= \(\hat{i}\) - 2\(\hat{j}\) + \(\hat{k}\) and \(\vec{P}\) = 2\(\hat{i}\) - \(\hat{j}\) +\(\hat{k}\). Its angular momentum about the origin is
- (a)
-\(\hat{i}\) +\(\hat{j}\) -3 \(\hat{k}\)
- (b)
-\(\hat{i}\) +\(\hat{j}\) +3 \(\hat{k}\)
- (c)
-\(\hat{i}\) -\(\hat{j}\) +3 \(\hat{k}\)
- (d)
-\(\hat{i}\) -\(\hat{j}\) -5 \(\hat{k}\)
- (e)
\(\hat{i}\) +\(\hat{j}\) +5 \(\hat{k}\)