Physical World and Measurement

1. A physical quantity of the dimensions of length that can be formed out of c, G and 𝑒2

4𝜋𝜀0

is [c is velocity of light, G is universal constant of gravitation and e is charge]. [NEET 2017]

(a) 1

𝐶2 [𝐺𝑒2

4𝜋𝜀0]

1/2

(b) 𝐶2 [𝐺𝑒2

4𝜋𝜀0]

1/2

(c) 1

𝐶2 [𝑒2

𝐺4𝜋𝜀0]

1/2

(d) 1

𝑐G

𝑒2

4𝜋𝜀0

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) [E𝑣−1𝑇−1]

(b) [E𝑣−1𝑇−2]

(c) [E𝑣−2𝑇−2]

(d) [𝐸−2𝑣−1𝑇−3]

3. If dimensions of circular velocity 𝑣𝑐of a liquid flowing through a tube are expressed as

[𝜂𝑥𝜌𝑦𝑟𝑧], where η , ρ 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, −1, −1

(b) 1, −1,1

(c) −1, −1, −1

(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 𝑇−1]

(b) [F v 𝑇−2]

(c) [F 𝑣−1 𝑇−1]

(d) [F 𝑣−1𝑇]

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= 𝑎3𝑏2

𝑐𝑑%. Error in P is

(a) 14%

(b) 10%

(c) 7%

(d) 4%

6. The dimensions of (𝜇0𝜀0)1/2are [CBSE AIPMT 2012]

(a) [𝐿1/2𝑇−1/2]

(b) [𝐿−1𝑇]

(c) [L𝑇−1]

(d) [𝐿1/2𝑇1/2]

7. The dimensions of1

2𝜀0𝐸2, where 𝜀0 is permittivity of free space and E is electric field are

[CBSE AIPMT 2010]

(a) [M𝐿2𝑇−2]

(b) [M𝐿−1𝑇−2]

(c) [M𝐿2𝑇−1]

(d) [M𝐿𝑇−1]

8. If the dimensions of a physical quantity are given by [𝑀𝑎𝐿𝑏𝑇𝑐], then the physical quantity

will be [CBSE AIPMT 2009]

(a) Pressure if 𝑎 = 1, 𝑏 = −1, 𝑐 = −2

(b) Velocity if 𝑎 = 1, 𝑏 = 0, 𝑐 = −1

(c) Acceleration if 𝑎 = 1, 𝑏 = 1, 𝑐 = −2

(d) Force if 𝑎 = 0, 𝑏 = −1, 𝑐 = −2

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) Young’s 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 current𝐼, would be [CBSE AIPMT 2007]

(a) [M𝐿2𝑇−3𝐼−1]

(b) [M𝐿2𝑇−2]

(c) [M𝐿2𝑇−1𝐼−1]

(d) [M𝐿2𝑇−3𝐼−2]

12. The velocity v of a particle at time t is given by v=at +𝑏

𝑡+𝑐, where a, b and c are constants.

The dimensions of a, b and c are respectively [CBSE AIPMT 2006]

(a) [𝐿𝑇−2], [𝐿]𝑎𝑛𝑑 [𝑇]

(b) [𝐿2], [𝑇]𝑎𝑛𝑑 [𝐿𝑇2]

(c) [𝐿𝑇2], [𝐿𝑇]𝑎𝑛𝑑 [𝐿]

(d) [𝐿], [𝐿𝑇]𝑎𝑛𝑑 [𝑇2]

13. The ratio of the dimensions of Planck’s 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) [𝑀−1𝐿3𝑇−2]

(b) [𝑀𝐿2𝑇−1]

(c) [𝑀−2𝐿3𝑇−2]

(d) [𝑀−2𝐿2𝑇−1]

15. The unit of permittivity of free space, 𝜀0is [CBSE AIPMT 2004]

(a) Coulomb/newton-metre

(b) Newton –metre 2/coulomb2

(c) Coulomb2/newton –metre 2

(d) Coulomb2/ (newton –metre)2

16. The value of Planck’s constant in SI unit is [CBSE AIPMT 2002]

(a) 6.63× 10−31𝐽 − 𝑠

(b) 6.63 × 10−30𝑘𝑔 − 𝑚/𝑠

(c) 6.63 × 10−32𝑘𝑔 − 𝑚2

(d) 6.63× 10−34𝐽 − 𝑠

17. Planck’s 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) [𝑀𝐿2𝑇−2𝐴−1]

(b) [𝑀𝐿3𝑇−2𝐴−2]

(c) [𝑀0𝐿−2𝑇2𝐴−2]

(d) [𝑀𝐿2𝑇−1𝐴2]

20. The force F on a sphere of radius r moving in a medium with velocity v is given by 𝐹 =

6𝜋𝜂𝑟𝑣. The dimensions of η are [CBSE AIPMT 1997]

(a) [𝑀𝐿−3]

(b) [𝑀𝐿𝑇−3]

(c) [𝑀𝐿−1]

(d) [𝑀𝐿−1𝑇−1]

21. Which of the following will have the dimensions of time ? [CBSE AIPMT 1996]

(a) LC

(b) 𝑅

𝐿

(c) 𝐿

𝑅

(d) 𝐶

𝐿

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 (𝑃 +𝑎

𝑣2) =b𝜃

𝑉, where p=pressure, V= volume and 𝜃 = absolute

temperature. If a and b are constants, then dimensions of a will be [CBSE AIPMT 1996]

(a) [𝑀𝐿5𝑇−2]

(b) [𝑀−1𝐿5𝑇2]

(c) [𝑀𝐿5𝑇−1]

(d) [𝑀𝐿5𝑇]

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) Poisson’s 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

100𝑁

(d) 1

(𝑁−1)

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

𝜂 =𝑝(𝑟2 − 𝑥2)

4𝑣𝑙

Where, v is the velocity of oil at distance x from the axis of the tube. The dimensions of

𝜂 are [CBSE AIPMT 1993]

(a) [𝑀0𝐿0𝑇0]

(b) [𝑀𝐿𝑇−1]

(c) [𝑀𝐿2𝑇−2]

(d) [𝑀𝐿−1𝑇−1]

29. The time dependence of physical quantity p is given by p=𝑝0exp (-𝛼𝑡2), where α is a

constant and t is the time. The constant α [CBSE AIPMT 1992]

(a) is dimensionless

(b) Has dimensions [𝑇−2]

(c) Has dimensions [𝑇2]

(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 𝑝𝑥𝑆𝑦𝑐𝑧 is

dimensionless are [CBSE AIPMT 1992]

(a) 𝑥 = 1, 𝑦 = 1, 𝑧 = 1

(b) 𝑥 = −1, 𝑦 = 1, 𝑧 = 1

(c) 𝑥 = 1, 𝑦 = −1, 𝑧 = 1

(d) 𝑥 = 1, 𝑦 = 1, 𝑧 = −1

31. The dimensional formula for permeability of free space 𝜇0 is [CBSE AIPMT 1991]

(a) [ML𝑇−2𝐴−2]

(b) [M𝐿−1𝑇2𝐴−2]

(c) [M𝐿−1𝑇2𝐴2]

(d) [ML𝑇−2𝐴−1]

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 𝑓 of a mass m suspended from a spring constant k is given by

a relation of the type 𝑓 = 𝐶𝑚𝑥𝑘𝑦,where C is a dimensionless constant. The values of x and

y are [CBSE AIPMT 19990]

(a) 𝑥 =1

2, 𝑦 =

1

2

(b) 𝑥 = −1

2, 𝑦 = −

1

2

(c) 𝑥 =1

2, 𝑦 = −

1

2

(d) 𝑥 = −1

2, 𝑦 =

1

2

34. According to Newton, the viscous force acting between liquid layers of area A and

velocity gradient ∆𝑣

∆𝑧 is given by F= −𝜂𝐴

𝑑𝑣

𝑑𝑧, where η is constant called [CBSEAIPMT1990]

(a) [𝑀𝐿−2𝑇−2]

(b) [𝑀0𝐿0𝑇0]

(c) [𝑀𝐿2𝑇−2]

(d) [𝑀𝐿−1𝑇−1]

35. The dimensional formula of pressure is [CBSE AIPMT 1990]

(a) [ML𝑇−2]

(b) [𝑀𝐿−1𝑇2]

(c) [𝑀𝐿−1𝑇−2]

(d) [ML𝑇2]

36. The dimensional formula of torque is [CBSE AIPMT 1989]

(a) [𝑀𝐿2𝑇−2]

(b) [ML𝑇−2]

(c) [𝑀𝐿−1𝑇−2]

(d) [𝑀𝐿−2𝑇−2]

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) [𝑀𝐿𝑇−2𝐴−2]

(b) [𝑀𝐿2𝑇−1𝐴−2]

(c) [𝑀𝐿2𝑇−2𝐴−2]

(d) [𝑀𝐿2𝑇−2𝐴−1]

39. If x=𝑎𝑡 + 𝑏𝑡2 , 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/𝑠2

(d) km-𝑠2

40. The dimensional formula for angular momentum is [CBSE AIPMT 1988]

(a) [𝑀0𝐿2𝑇−2]

(b) [𝑀𝐿2𝑇−1]

(c) [𝑀𝐿𝑇−1]

(d) [𝑀𝐿2𝑇−2]

41. If C and R denote capacitance and resistance respectively , then the dimensional formula

of CR is [CBSE AIPMT 1988]

(a) [𝑀0𝐿0𝑇]

(b) [𝑀0𝐿0𝑇0]

(c) [𝑀0𝐿0𝑇−1]

(d) Not expressible in terms of [MLT]