Q.1
While measuring the length of a cylinder by vernier callipers, the MSR is found to be 4.6 cm and 6th vernier division on the main scale. If the least count of the vernier is 0.01 cm and zero error is –0.02 cm then the length of the cylinder is
  • a) 4.56 cm
  • b) 4.68 cm
  • c) 4.64 cm
  • d) 4.66 cm
Q.2
If force (F), velocity(V) and time (T) are takenas fundamental units, then the dimensions of mass are
  • a) [F V–1 T–1]
  • b) [F V–1 T]
  • c) [F V T–1]
  • d) [F V T–2]
Q.3
If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensionalformula of surface tension will be :
  • a) [E-2 V-1 T-3]
  • b) [E V-2 T-1]
  • c) [E V-1 T-2]
  • d) [E V-2 T-2]
Q.4
In dimension of critical velocity νc, of liquid flowing through a tube are expressed as (ηxρyrz), whereη, 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 :
  • a) 1, 1, 1
  • b) 1, -1, -1
  • c) -1, -1, 1
  • d) -1, -1, -1
Q.5
Planck's constant (h), speed of light in vacuum (c)and Newton's gravitational constant (G) are threefundamental constants. Which of the followingcombinations of these has the dimension of length?
  • a)
  • b)
  • c)
  • d)
Q.6
A physical quantity of the dimensions of length thatcan be formed out of c, G and is [c is velocityof light, G is universal constant of gravitation and e is charge] …[ NEET 2017]
  • a)
    ch-1_qn-260choice_img_no1.png
  • b)
    ch-1_qn-260choice_img_no2.png
  • c)
    ch-1_qn-260choice_img_no3.png
  • d)
    ch-1_qn-260choice_img_no4.png
Q.7
The energy of a system as a function of time t is given as E(t) = A2 exp(-αt), where α = 0.2 s-The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of E(t) at t = 5 s is … [ IIT Advance 2015]
  • a) 2
  • b) 4
  • c) 6
  • d) 8
Q.8
1 g = ... amu
  • c) 6.024 ×1023
  • a) 6.024 × 10⁻²⁹
  • b) 1.66 ×10⁻³⁰
  • d) 1.66 ×10⁻²⁴
Q.9
Let [ε0] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = Time and A = electric current, then …. [ IIT Mains -2016]
ch-1_que_no-261_img_no1.png
  • a) [ε0] = [M−1 L−3 T2 A]
    ch-1_qn-261choice_img_no1.png
  • b) [ε0] = [M−1 L−3 T4 A2]
    ch-1_qn-261choice_img_no2.png
  • c) [ε0] = [M−1 L2 T−1 A−2]
    ch-1_qn-261choice_img_no3.png
  • d) [ε0] = [M−1 L2 T−1 A]
    ch-1_qn-261choice_img_no4.png
Q.10
The diameter of a cylinder is measured using a Vernier caliper with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is
  • a) 5.112 cm
  • b) 5.124 cm
  • c) 5.136 cm
  • d) 5.148 cm
Q.11
)Using the expression 2d sin θ = λ, one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90º. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0°.
  • a) the absolute error in d remains constant.
  • b) the absolute error in d increases.
  • c) the fractional error in d remains constant.
  • d) the fractional error in d decreases.
Q.12
)Match List I with List II and select the correct answer using the codes given below the lists:
List I List II
P. Boltzmann constant [ML2T−1]
Q. Coefficient of viscosity [ML−1T−1]
R. Planck constant [MLT−3T−1]
S. Thermal conductivity [ML2T−2K−1]
  • b) P → 3 ; Q → 2 ; R → 1 ; S → 4
  • a) P → 3 ; Q → 1 ; R → 2 ; S → 4
  • c) P → 4 ; Q → 2 ; R → 1 ; S → 3
  • d) P → 4 ; Q → 1 ; R → 2 ; S → 3
Q.13
To find the distance d over which a signal can be seen clearly in foggyconditions, arailways engineer uses dimensional analysis and assumes that the distance depends on themass density ρ of the fog, intensity (power/area) S of the light from the signal and itsfrequency f. The engineer finds that d is proportional to S1/n. The value of n is … [ IIT Advance 2014]
  • a) 1
  • b) 2
  • c) 3
  • d) 4
Q.14
Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equaldivisions and a screw gauge with 100 divisions on its circular scale. In the Verniercallipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale andin the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then …[ IIT Advance 2015]
  • a) If the pitch of the screw gauge is twice the least count of the Vernier callipers, theleast count of the screw gauge is 0.01 mm
  • b) If the pitch of the screw gauge is twice the least count of the Vernier callipers, theleast count of the screw gauge is 0.005 mm.
  • c) If the least count of the linear scale of the screw gauge is twice the least count of theVernier callipers, the least count of the screw gauge is 0.01 mm.
  • d) If the least count of the linear scale of the screw gauge is twice the least count of theVernier callipers, the least count of the screw gauge is 0.005 mm.
Q.15
than one correct answer Q269) Planck's constant h, speed of light c and gravitational constant G are used to form a unit oflength L and a unit of mass M. Then the correct option(s) is(are) ... [IIT Advance 2016]
  • a) M ∝ √ c
  • b) M ∝ √G
  • c) L ∝ √h
  • d) L ∝ √G
Q.16
In terms of potential difference V, electric current I, permittivity &epslon0 , permeability µ0 and speed of light c, the dimensionally correct equation(s) is(are) [ IIT Advance 2015]
  • a) µ0 I2 = ε0 V2
  • b) ε0I = µ0V
  • c) I = ε0 cV
  • d) µ0cI = ε0 V
Q.17
A length-scale (l) depends on the permittivity (ε) of a dielectric material, Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for is(are) dimensionally correct? [ IIT Advance 2016]
  • a)
  • b)
  • c)
  • d)
Q.18
There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers (C1) has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper (C2) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers C1 and C2, respectively, are .. [IIT Advance 2016]
  • a) 2.87 and 2.86
    ch-1_qn-272choice_img_no1.png
  • b) 2.85 and 2.82
    ch-1_qn-272choice_img_no2.png
  • c) 2.87 and 2.87
    ch-1_qn-272choice_img_no3.png
  • d) 2.87 and 2.83
    ch-1_qn-272choice_img_no4.png
Q.19
than one correct answer Q274) In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is = 2π . The values of R and r are measured to be (60 ± 1) mm and (10 ± 1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true? [ IIT Advance 2016]
ch-1_que_no-273_img_no1.png
  • a) The error in the measurement of r is 10%
  • b) The error in the measurement of T is 3.57%
  • c) The error in the measurement of T is 2%
  • d) The error in the determined value of g is 11%
Q.20
A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is δT = 0.01 second and he measures the depth of the well to be L = 20 meters. Take the acceleration due to gravity g = 10 ms–2 and the velocity of sound is 300 ms–Then the fractional error in the measurement, &deltaL/L, is closest to
ch-1_que_no-274_img_no1.png
  • a) 0.2 %
  • b) 5 %
  • c) 3 %
  • d) 1 %
Q.21
103 g/cm³ = ... .. kg/m³
  • a) 10-6
  • b) 101
  • c) 103
  • d) 106
Q.22
In M.K.S. system, if the value of gravitational constant is 6.67 × 10⁻¹¹Nm2 kg-2 then what is its value in .... ... dyne cm2 g-2, i c.g.s system 1kg = 103 gm Answer : (b)
  • a) 6.67 ×10⁻⁷
  • b) 6.67 ×10⁻⁸
  • c) 6.67 ×10⁻⁹
  • d) 6.67 ×10⁻¹⁰
Q.23
The Sun's angular diameter is measured to be 1920". if the distance of the earth from sun is 1.896×1011m then the diameter of the sun is ... (1"=4.85×10⁻⁶ rad)
  • a) 1.766 ×109 m
  • b) 1.766 ×1011 m
  • c) 1.393 ×109 m
  • d) 1.496 ×1011 m
Q.24
A cube has a side of length 1.2×10-Calculate its volume .. [ CBSE-PMT 2003]
  • a) 1.7×10⁻⁶ m³
  • b) 1.73×10⁻⁶ m³
  • c) 1.70×10⁻⁶ m³
  • d) 1.732×10⁻⁶ m³
Q.25
The result of adding 3.6×10⁻⁶ and 2.2×10⁻⁵ with due regard to significant figure is
  • a) 38.2×10⁻⁵
  • b) 2.6×10⁻⁵
  • c) 3.8×10⁻⁶
  • d) 2.6×10⁻⁶
Q.26
Add 3.8 ×10⁻⁶ to 4.2 ×10⁻⁵ with due regards to significant figure
  • a) 4.6 ×10⁻⁵
  • b) 4.6 ×10⁻⁶
  • c) 4.58 ×10⁻⁵
  • d) 4.580 ×10⁻⁵
Q.27
If the length of a cylinder is l = (4.00 ± 0.01) cm, radius r = ( 0.250 ±0.001) cm and mass m = ( 6.25 ± 0.01) g. Calculate the percentage error in determination of density... .. [ Guj T.B.]
  • a) 12%
  • b) 11.2%
  • c) 1.21%
  • d) 12.1%
Q.28
The acceleration due to gravity (g) is determined by using simple pendulum of length l = (100 ± 0.1 ) cm. if the time period is T = (2 ± 0.01 )s, find the maximum percentage error in the measurement of g
  • a) 21%
  • b) 0.0021%
  • c) 0.011 %
  • d) 1.1 %
Q.29
Wave length of visible light is 0.00006 m then it is =...
  • a) 6 microm
  • b) 60 micron
  • c) 600 micron
  • d) 0.6 micron
Q.30
During Searle’s experiment, zero of the Vernier scale lies between 3.20 × 10⁻² m and3.25 × 10⁻² m of the main scale. The 20th division of the Vernier scale exactly coincideswith one of the main scale divisions. When an additional load of 2 kg is applied to thewire, the zero of the Vernier scale still lies between 3.20 × 10⁻²m and 3.25 × 10⁻² m of themain scale but now the 45th division of Vernier scale coincides with one of the main scaledivisions. The length of the thin metallic wire is 2 m and its cross−sectional area is 8 × 10⁻⁷ mThe least count of the Vernier scale is 1.0 × 10⁻⁵m. The maximum percentageerror in the Young’s modulus of the wire is ..[ IIT Advance 2014]
  • a) 2
  • b) 6
  • c) 5
  • d) 8
0 h : 0 m : 1 s