Post on 24-Jan-2023
Physical World and Measurement
1. A physical quantity of the dimensions of length that can be formed out of c, G and ๐2
4๐๐0
is [c is velocity of light, G is universal constant of gravitation and e is charge]. [NEET 2017]
(a) 1
๐ถ2 [๐บ๐2
4๐๐0]
1/2
(b) ๐ถ2 [๐บ๐2
4๐๐0]
1/2
(c) 1
๐ถ2 [๐2
๐บ4๐๐0]
1/2
(d) 1
๐G
๐2
4๐๐0
2. If the energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the
dimensional formula of surface tension will be [CBSE AIPMT 2015]
(a) [E๐ฃโ1๐โ1]
(b) [E๐ฃโ1๐โ2]
(c) [E๐ฃโ2๐โ2]
(d) [๐ธโ2๐ฃโ1๐โ3]
3. If dimensions of circular velocity ๐ฃ๐of a liquid flowing through a tube are expressed as
[๐๐ฅ๐๐ฆ๐๐ง], where ฮท , ฯ and r are the coefficient of viscosity of liquid, density of liquid and
radius of the tube respectively, then the values of x, y and z are given by
[CBSEAIPMT2015]
(a) 1, โ1, โ1
(b) 1, โ1,1
(c) โ1, โ1, โ1
(d) 1, 1, 1
4. If force (F), velocity (v) and time (T) are taken as fundamental units , then the dimensions
of mass are [CBSE AIPMT 2014]
(a) [F v ๐โ1]
(b) [F v ๐โ2]
(c) [F ๐ฃโ1 ๐โ1]
(d) [F ๐ฃโ1๐]
5. In an experiment, four quantities a, b, c and d are measured with percentage error 1% ,
2%, 3% and 4% respectively . Quantity P is calculated P= ๐3๐2
๐๐%. Error in P is
(a) 14%
(b) 10%
(c) 7%
(d) 4%
6. The dimensions of (๐0๐0)1/2are [CBSE AIPMT 2012]
(a) [๐ฟ1/2๐โ1/2]
(b) [๐ฟโ1๐]
(c) [L๐โ1]
(d) [๐ฟ1/2๐1/2]
7. The dimensions of1
2๐0๐ธ2, where ๐0 is permittivity of free space and E is electric field are
[CBSE AIPMT 2010]
(a) [M๐ฟ2๐โ2]
(b) [M๐ฟโ1๐โ2]
(c) [M๐ฟ2๐โ1]
(d) [M๐ฟ๐โ1]
8. If the dimensions of a physical quantity are given by [๐๐๐ฟ๐๐๐], then the physical quantity
will be [CBSE AIPMT 2009]
(a) Pressure if ๐ = 1, ๐ = โ1, ๐ = โ2
(b) Velocity if ๐ = 1, ๐ = 0, ๐ = โ1
(c) Acceleration if ๐ = 1, ๐ = 1, ๐ = โ2
(d) Force if ๐ = 0, ๐ = โ1, ๐ = โ2
9. Which two of the following five physical parameters have the same dimensions?
[CBSEAIPMT 2008]
(i) Energy density
(ii) Refractive index
(iii) Dielectric constant
(iv) Youngโs modulus
(v) Magnetic field
(a) (ii) and (iv)
(b) (iii) and (v)
(c) (i) and (iv)
(d) (i) and (v)
10. If the error in the measurement of radius of a sphere is 2%, then the error in the
determination of volume of the sphere will be [CBSE AIPMT 2008]
(a) 4%
(b) 6%
(c) 8%
(d) 2%
11. Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of
length L, of time T and of current๐ผ, would be [CBSE AIPMT 2007]
(a) [M๐ฟ2๐โ3๐ผโ1]
(b) [M๐ฟ2๐โ2]
(c) [M๐ฟ2๐โ1๐ผโ1]
(d) [M๐ฟ2๐โ3๐ผโ2]
12. The velocity v of a particle at time t is given by v=at +๐
๐ก+๐, where a, b and c are constants.
The dimensions of a, b and c are respectively [CBSE AIPMT 2006]
(a) [๐ฟ๐โ2], [๐ฟ]๐๐๐ [๐]
(b) [๐ฟ2], [๐]๐๐๐ [๐ฟ๐2]
(c) [๐ฟ๐2], [๐ฟ๐]๐๐๐ [๐ฟ]
(d) [๐ฟ], [๐ฟ๐]๐๐๐ [๐2]
13. The ratio of the dimensions of Planckโs constant and that of the moment of inertia is the
dimension of [CBSE AIPMT 2005]
(a) Frequency
(b) Velocity
(c) Angular momentum
(d) Time
14. The dimensions of universal gravitational constant are [CBSE AIPMT 2004, 1992]
(a) [๐โ1๐ฟ3๐โ2]
(b) [๐๐ฟ2๐โ1]
(c) [๐โ2๐ฟ3๐โ2]
(d) [๐โ2๐ฟ2๐โ1]
15. The unit of permittivity of free space, ๐0is [CBSE AIPMT 2004]
(a) Coulomb/newton-metre
(b) Newton โmetre 2/coulomb2
(c) Coulomb2/newton โmetre 2
(d) Coulomb2/ (newton โmetre)2
16. The value of Planckโs constant in SI unit is [CBSE AIPMT 2002]
(a) 6.63ร 10โ31๐ฝ โ ๐
(b) 6.63 ร 10โ30๐๐ โ ๐/๐
(c) 6.63 ร 10โ32๐๐ โ ๐2
(d) 6.63ร 10โ34๐ฝ โ ๐
17. Planckโs constant has the dimensions of [CBSE AIPMT 2001]
(a) Linear momentum
(b) Angular momentum
(c) Energy
(d) Power
18. A pair of physical quantities having same dimensional formula is [CBSE AIPMT 2000]
(a) Force and torque
(b) Work and energy
(c) Force and impulse
(d) Linear momentum and angular momentum
19. The dimensional formula for magnetic flux is [CBSE AIPMT 1999]
(a) [๐๐ฟ2๐โ2๐ดโ1]
(b) [๐๐ฟ3๐โ2๐ดโ2]
(c) [๐0๐ฟโ2๐2๐ดโ2]
(d) [๐๐ฟ2๐โ1๐ด2]
20. The force F on a sphere of radius r moving in a medium with velocity v is given by ๐น =
6๐๐๐๐ฃ. The dimensions of ฮท are [CBSE AIPMT 1997]
(a) [๐๐ฟโ3]
(b) [๐๐ฟ๐โ3]
(c) [๐๐ฟโ1]
(d) [๐๐ฟโ1๐โ1]
21. Which of the following will have the dimensions of time ? [CBSE AIPMT 1996]
(a) LC
(b) ๐
๐ฟ
(c) ๐ฟ
๐
(d) ๐ถ
๐ฟ
22. The density of a cube is measured by measuring its mass and length of its sides. If the
maximum error in the measurement of mass and length are 4% and 3% respectively, the
maximum error in the measurement of density will be [CBSE AIPMT 1996]
(a) 7%
(b) 9%
(c) 12%
(d) 13%
23. An equation is given as (๐ +๐
๐ฃ2) =b๐
๐, where p=pressure, V= volume and ๐ = absolute
temperature. If a and b are constants, then dimensions of a will be [CBSE AIPMT 1996]
(a) [๐๐ฟ5๐โ2]
(b) [๐โ1๐ฟ5๐2]
(c) [๐๐ฟ5๐โ1]
(d) [๐๐ฟ5๐]
24. The percentage errors in the measurement of mass and speed are 2% and 3%
respectively. The error is kinetic energy obtained by measuring mass and speed will be
[CBSE AIPMT 1995]
(a) 12%
(b) 10%
(c) 8%
(d) 2%
25. Which of the following is a dimensional constant? [CBSE AIPMT 1995]
(a) Refractive index
(b) Poissonโs ratio
(c) Relative density
(d) Gravitational constant
26. In a vernier callipers N divisions of vernier scale coincide with N-1 divisions of main scale
(in which length of one division is 1mm). The least count of the instrument should be:
(a) N
(b) N-1
(c) 1
100๐
(d) 1
(๐โ1)
27. In a particular system, the unit of length, mass and time are chosen to be 10cm, 10g and
0.1 s respectively. The unit of force in this system will be equivalent to [CBSE AIPMT 1994]
(a) 0.1N
(b) 1N
(c) 10N
(d) 100N
28. Turpentine oil is flowing through the tube of length l and radius r. The pressure
difference between the two ends of the tube is p. The viscosity of oil is given by
๐ =๐(๐2 โ ๐ฅ2)
4๐ฃ๐
Where, v is the velocity of oil at distance x from the axis of the tube. The dimensions of
๐ are [CBSE AIPMT 1993]
(a) [๐0๐ฟ0๐0]
(b) [๐๐ฟ๐โ1]
(c) [๐๐ฟ2๐โ2]
(d) [๐๐ฟโ1๐โ1]
29. The time dependence of physical quantity p is given by p=๐0exp (-๐ผ๐ก2), where ฮฑ is a
constant and t is the time. The constant ฮฑ [CBSE AIPMT 1992]
(a) is dimensionless
(b) Has dimensions [๐โ2]
(c) Has dimensions [๐2]
(d) Has dimensions of p
30. If p represents radiation pressure, c represents speed of light and S represents radiation
energy striking unit area per sec. The non -zero integers x, y and z such that ๐๐ฅ๐๐ฆ๐๐ง is
dimensionless are [CBSE AIPMT 1992]
(a) ๐ฅ = 1, ๐ฆ = 1, ๐ง = 1
(b) ๐ฅ = โ1, ๐ฆ = 1, ๐ง = 1
(c) ๐ฅ = 1, ๐ฆ = โ1, ๐ง = 1
(d) ๐ฅ = 1, ๐ฆ = 1, ๐ง = โ1
31. The dimensional formula for permeability of free space ๐0 is [CBSE AIPMT 1991]
(a) [ML๐โ2๐ดโ2]
(b) [M๐ฟโ1๐2๐ดโ2]
(c) [M๐ฟโ1๐2๐ด2]
(d) [ML๐โ2๐ดโ1]
32. A certain body weighs 22.42g has a measured volume of 4.7 cc. The possible error in the
measurement of mass and volume are 0.01 g and 0.1. cc. Then, maximum error in the
density will be [CBSE AIPMT 19991]
(a) 22%
(b) 2%
(c) 0.2 %
(d) 0.02 %
33. The frequency of vibration ๐ of a mass m suspended from a spring constant k is given by
a relation of the type ๐ = ๐ถ๐๐ฅ๐๐ฆ,where C is a dimensionless constant. The values of x and
y are [CBSE AIPMT 19990]
(a) ๐ฅ =1
2, ๐ฆ =
1
2
(b) ๐ฅ = โ1
2, ๐ฆ = โ
1
2
(c) ๐ฅ =1
2, ๐ฆ = โ
1
2
(d) ๐ฅ = โ1
2, ๐ฆ =
1
2
34. According to Newton, the viscous force acting between liquid layers of area A and
velocity gradient โ๐ฃ
โ๐ง is given by F= โ๐๐ด
๐๐ฃ
๐๐ง, where ฮท is constant called [CBSEAIPMT1990]
(a) [๐๐ฟโ2๐โ2]
(b) [๐0๐ฟ0๐0]
(c) [๐๐ฟ2๐โ2]
(d) [๐๐ฟโ1๐โ1]
35. The dimensional formula of pressure is [CBSE AIPMT 1990]
(a) [ML๐โ2]
(b) [๐๐ฟโ1๐2]
(c) [๐๐ฟโ1๐โ2]
(d) [ML๐2]
36. The dimensional formula of torque is [CBSE AIPMT 1989]
(a) [๐๐ฟ2๐โ2]
(b) [ML๐โ2]
(c) [๐๐ฟโ1๐โ2]
(d) [๐๐ฟโ2๐โ2]
37. OF the following quantities, which one has dimensions different from the remaining
three? [CBSE AIPMT 1989]
(a) Energy per unit volume
(b) Force per unit area
(c) Product of voltage and charge per unit volume
(d) Angular momentum
38. Dimensional formula of self -inductance is [CBSE AIPMT 1989]
(a) [๐๐ฟ๐โ2๐ดโ2]
(b) [๐๐ฟ2๐โ1๐ดโ2]
(c) [๐๐ฟ2๐โ2๐ดโ2]
(d) [๐๐ฟ2๐โ2๐ดโ1]
39. If x=๐๐ก + ๐๐ก2 , where x is the distance travelled by the body in kilometre while t is the
time in second, then the unit of b is [CBSE AIPMT 1989]
(a) km/s
(b) km-s
(c) km/๐ 2
(d) km-๐ 2
40. The dimensional formula for angular momentum is [CBSE AIPMT 1988]
(a) [๐0๐ฟ2๐โ2]