Problems Based On Units and Dimensions
Problems Based On Units and Dimensions
Problems Based On Units and Dimensions
R
4. The dimension of are [MP PET 2003]
L
(a) [ML2 T 2 Q 1 ] (b) [MLT 2 Q 1 ] (c) ML2T 1Q (d) ML2T 2Q
7. The physical quantities not having same dimensions are [AIEEE 2003]
(c) Momentum and Planck's constant (d) Stress and Young's modulus
(a) [ML2 T 2 1 ] (b) [ML2 T 2 ] (c) [ML0 T 2 1 ] (d) [ML2 T 1 1 ]
(a) Gravitational constant (b) Planck's constant (c) Power of a convex lens (d) None of these
(a) Force per unit volume (b) Energy per unit volume (c) Force (d) Energy
12. Identify the pair whose dimensions are equal [AIEEE 2002]
(a) Torque and work (b) Stress and energy (c) Force and stress (d) Force and work
13. A physical quantity x depends on quantities y and z as follows: x Ay B tan Cz , where A, B and C are constants. Which of the
15. Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful [CPMT
1997]
16. Let [ 0 ] denotes the dimensional formula of the permittivity of the vacuum and [ 0 ] that of the permeability of the
0 LV
18. The quantity X ; here 0 is the permittivity of free space, L is length, V is potential difference and t is time. The
t
dimensions of X are same as that of
19. The unit of permittivity of free space 0 is [MP PET 1993; MP PMT 2003]
20. Dimensional formula of capacitance is [CPMT 1978; MP PMT 1979; IIT-JEE 1983]
21. The dimensional formula for impulse is [EAMCET 1981; CBSE PMT 1991; CPMT 1978; AFMC 1998; BCECE 2003]
22. The dimensions of universal gravitational constant are [MP PMT 1984, 87, 97, 2000; CBSE PMT 1988, 92, 2004; MP PET 1984, 96, 99;
MNR 1992; DPMT 1984; CPMT 1978, 84, 89, 90, 92, 96; AFMC 1999; NCERT 1975; DPET 1993; AIIMS 2002; RPET 2001;
82 Units, Dimensions and Measurement
23. How many wavelength of Kr 86 are there in one metre [MNR 1985; UPSEAT 2000]
24. Light year is a unit of [MP PMT 1989; AFMC 1991; CPMT 1991]
25. L, C and R represent physical quantities inductance, capacitance and resistance respectively. The combination which has the
dimensions of frequency is [IIT-JEE 1984]
27. If the acceleration due to gravity be taken as the unit of acceleration and the velocity generated in a falling body in one second as
the unit of velocity then
(a) The new unit of length is g metre (b) The new unit of length is 1 metre
1
(c) The new unit of length is g 2 metre (d) The new unit of time is second
g
28. The famous Stefan's law of radiation states that the rate of emission of thermal radiation per unit by a black body is proportional
to area and fourth power of its absolute temperature that is Q AT 4 where A area, T temperature and is a universal
constant. In the 'energy- length- time temperature' (E-L-T-K) system the dimension of is
29. The resistive force acting on a body moving with a velocity V through a fluid at rest is given by F C D V 2 A
where, CD = coefficient of drag, A = area of cross-section perpendicular to the direction of motion. The
dimensions of CD are
(a) ML3T– 2 (b) M-1L– 1T2 (c) M-1 L–1 T–2 (d) M0L0T0
(a) [M3 LT– 2A2] (b) [MA– 1 T– 1] (c) [ML2A– 2 T] (d) [M2 L–3AT2]
P F
31. The frequency n of vibrations of uniform string of length l and stretched with a force F is given by n where p is the
2l m
number of segments of the vibrating string and m is a constant of the string. What are the dimensions of m
(a) A dimensionally correct equation may be correct (b) A dimensionally correct equation may be incorrect
(c) A dimensionally incorrect equation may be incorrect (d) A dimensionally incorrect equation may be incorrect
Kr
33. A certain body of mass M moves under the action of a conservative force with potential energy V given by V where x
x a 2'
2
34. The Richardson equation is given by I AT 2 e B / kT . The dimensional formula for AB2 is same as that for
35. If the units of force, energy and velocity are 10 N, 100 J and 5 ms–1, the units of length, mass and time will be
(a) 10m, 5kg, 1s (b) 10m, 4kg, 2s (c) 10m, 4kg, 0.5s (d) 20m, 5kg, 2s.
l
36. The period of oscillation of a simple pendulum is given by T 2 where l is about 100 cm and is known to 1mm accuracy. The
g
period is about 2s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is
37. The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error
in the estimation of the kinetic energy obtained by measuring mass and speed [NCERT 1990; Orissa JEE 1990]
38. While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the
pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation
g 4 2 l / T 2 will be
39. The random error in the arithmetic mean of 100 observations is x; then random error in the arithmetic mean of 400 observations
would be
1 1
(a) 4x (b) x (c) 2x (d) x
4 2
41. Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is
42. The mean time period of second's pendulum is 2.00s and mean absolute error on the time period is 0.05s. To express maximum
(a) (2.00 0.01) s (b) (2.00 +0.025) s (c) (2.00 0.05) s (d) (2.00 0.10) s
43. A body travels uniformly a distance of (13.8 0.2) m in a time (4.0 0.3) s. The velocity of the body within error limits is
(a) (3.45 0.2) ms-1 (b) (3.45 0.3) ms-1 (c) (3.45 0.4) ms-1 (d) (3.45 0.5) ms-1
(d) Errors have got their own units which are different from that of physical quantity measured
47. If 97.52 is divided by 2.54, the correct result in terms of significant figures is
(a) Absolute error (b) Percentage error (c) Both (d) None of these
49. The radius of a sphere is (5.3 0.1) cm. The percentage error in its volume is
0 .1 0 .1 0 .1 100 0 .1
(a) 100 (b) 3 100 (c) (d) 3 100
5 .3 5 .3 3 .53 5 .3
50. A thin copper wire of length l metre increases in length by 2% when heated through 10ºC. What is the percentage increase in area
51. In the context of accuracy of measurement and significant figures in expressing results of experiment, which of the following is/are
correct
(1) Out of the two measurements 50.14 cm and 0.00025 ampere, the first one has greater accuracy
(2) If one travels 478 km by rail and 397 m. by road, the total distance travelled is 478 km.
(a) Only (1) is correct (b) Only (2) is correct (c) Both are correct (d) None of them is correct.
84 Electrostatics
51.
c