458 + Interview Questions in MEASUREMENTS IN GENERAL AWARENESS Page 2 InterviewSolution

51.	What is the dimensional formula for pressure gradient?A. `[M^(1)L^(2)T^(-1)]`B. `[M L^(-2)T^(-2)]`C. `[M^(-2)L^(-2)T^(0)]`D. `[M^(0)L^(2)T^(-2)]`
Answer» Correct Answer - b Pressure gradient `=("Difference in pressure")/("Distance between the two points")=(dP)/(dx)` `therefore ["Pressure gradient"]=[(dP)/(dx)]=[(F//A)/(L)]=[(M^(1)L^(1)T^(-2))/(L^(2)xxL)]` `=[M^(1)L^(-2)T^(-2)]`

Discussion

52.	Which one of the following gives the dimensional formula of coefficient of friction?A. `[M LT^(-2)]`B. `[M^(2)LT^(-2)]`C. `[M^(0)L^(0)T^(0)]`D. `[M^(2)LT]`
Answer» Correct Answer - c Coefficient of friction = `("Frictional force")/("Normal reaction")=(F)/(R )` `therefore [mu]=[(F)/(R)]=[(M^(1)L^(1)T^(-2))/(M^(1)L^(1)T^(-2))]=[M^(0)L^(0)T^(0)]` Normal reaction is also a force. `mu` is a dimensionless quantity.

Discussion

53.	Which one of the following gives the dimensional formula of coefficient of friction?A. `[MLT^(-2)]`B. `[M^(2)LT^(-2)]`C. `[M^(0)L^(0)T^(0)]`D. `[M^(2)LT]`
Answer» Correct Answer - C Coefficient of friction = `("Frictional force")/("Normal reaction")=(F)/(R )` `therefore [mu]=[(F)/(R)]=[(M^(1)L^(1)T^(-2))/(M^(1)L^(1)T^(-2))]=[M^(0)L^(0)T^(0)]` Normal reaction is also a force. `mu` is a dimensionless quantity.

Discussion

54.	What is the dimensional formula of specific resistance in terms of charge Q?A. `M^(1)L^(2)T^(-2)Q^(-1)`B. `M^(1)L^(2)T^(-2)Q^(-2)`C. `M^(1)L^(3)T^(-1)Q^(-2)`D. `M^(1)L T^(-2)Q^(-1)`
Answer» Correct Answer - c `R=(rhoL)/(A) therefore rho=(RA)/(L)=(V)/(I)(A)/(L)" "(because R=(V)/(I))` But `I=Q//t and V=(W)/(Q)` `therefore rho=(W)/(Q)xx(A)/(L)xx(t)/(Q)=(WAt)/(Q^(2)L)` `because [rho]=(M^(1)L^(2)T^(-2)xxL^(2)xxT^(1))/(Q^(2)xxL^(1))` `therefore [rho]=[M^(1)L^(3)T^(-1)Q^(-2)]`

Discussion

55.	Given the specific gravity of gold as 19 the mass of 100 cm volume of gold is `"______"` kg
Answer» Correct Answer - 1.9

Discussion

56.	S.I. unit of specific resistance is(A) Ω cm (B) Ω m (C) Ω/cm (D) mho-cm
Answer» Answer is (B) Ω m

Discussion

57.	S. I unit of principle specific heat is(A) kcal/gm K (B) cal/gm K (C) J/kg K (D) erg/kg K
Answer» Answer is (C) J/kg K

Discussion

58.	The S.I. units of the constant in Wein’s displacement law are(A) cm K-1 (B) mK (C) cm2 K-1 (D) cm K-2
Answer» Answer is (B) mK

Discussion

59.	The error in the measurement of length (L) of the simple pendulum is 0.1% and the error in time period (T) is 3%. The maximum possible error in the measurement of \(\frac{L}{T^2}\) is(A) 2.9% (B) 3.1% (C) 5.9% (D) 6.1%
Answer» Answer is (D) 6.1% Maximum possible error in measurement of \(\frac{L}{T^2}\) = \(\Big(\frac{ΔL}{L}+2\frac{ΔT}{T}\Big)\)% = (0.1 + 2 x 3) % = 6.1%

59.

The error in the measurement of length (L) of the simple pendulum is 0.1% and the error in time period (T) is 3%. The maximum possible error in the measurement of \(\frac{L}{T^2}\) is(A) 2.9% (B) 3.1% (C) 5.9% (D) 6.1%

Answer»

Answer is (D) 6.1%

Maximum possible error in measurement of

\(\frac{L}{T^2}\) = \(\Big(\frac{ΔL}{L}+2\frac{ΔT}{T}\Big)\)%

= (0.1 + 2 x 3) % = 6.1%

Discussion

60.	The error in the measurement of the radius of a sphere is `1%`. Find the error in the measurement of volume.A. `1%`B. `2%`C. `3%`D. `5%`
Answer» Correct Answer - c If the error in x is `deltax`, then the percentage error in `x^(n)` is `n((deltax)/(x))xx100%`. For a sphere `V=(4)/(3)pir^(3)` In this case x = r and n = 3 and `((dx)/(x))=(1)/(100)`. `therefore` Percentage error `=3((1)/(100))xx100%=3%`

Discussion

61.	Assertion (A): The masss of `150 m^(3)` of iron is greater than the mass of 150 m^(3) of wood. Reason (R): The densiy of iron is less than the density of wood.A. (a) Both A and R are true and R is the correct explanation of A.B. (b) Both A and R are true, but R is not the correct explanation of A.C. (c ) A is true but R is false.D. (d) Both A and R are false.
Answer» Correct Answer - C The mass of 150 `m^(3)` of iron is greater than the mass of 150 `m^(3)` of wood because the density of iron is greater than the density of wood. But the reason given is density of iron is less than the density of wood. So, A is correct and r is incorrect.

Discussion

62.	The base of the parallelogram is 16 cm and the height is 7 cm less than its base. Find the area of the parallelogram.
Answer» In a parallelogram Given base b = 16 cm; height h = base – 7 cm = 16 – 7 = 9 cm Area of the parallelogram = (base x height) sq. units = 16 x 9 cm² = 144 cm² Area of the parallelogram = 144 cm²

62.

The base of the parallelogram is 16 cm and the height is 7 cm less than its base. Find the area of the parallelogram.

Answer»

In a parallelogram

Given base b = 16 cm; height h = base – 7 cm = 16 – 7 = 9 cm

Area of the parallelogram = (base x height) sq. units

= 16 x 9 cm² = 144 cm²

Area of the parallelogram = 144 cm²

Discussion

63.	The dimensions of `1/2 in_(0) E^(2)` (`in_(0)`: permittivity of free space, E: electric field) is-A. `[ML^(2)T^(-1)]`B. `[ML^(-1)T^(-2)]`C. `[ML^(2)T^(-2)]`D. `[MLT^(-1)]`
Answer» Correct Answer - B `(1)/(2)epsi_(0)E^(2)="Energy density"=("Energy")/("Volume")` `implies([ML^(2)T^(-2)])/([L^(3)])=[ML^(-1)T^(-2)]`

Discussion

64.	A student uses a metre scale, measuring upto 1 mm, to measure the length and breadth of a rectangular plate. He finds that length = 5.7 cm and breadth = 3.4 cm. What is the percentage error in the area of the plate ?A. `3.5%`B. `4.7%`C. `5.3%`D. `6.2%`
Answer» Correct Answer - b Area of the plate = `A=lxxb` and `deltal=deltab=1` mm = 0.1 cm The percentage error in A is given by `((deltaA)/(A))xx100=((deltal)/(l))xx100+((deltab)/(b))xx100` `therefore ((deltaA)/(A))xx100=((0.1)/(5.7))xx100+((0.1)/(3.4))xx100` `=1.8%+2.9%=4.7%` [The figures are rounded of to the first decimal place.]

Discussion

65.	A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickenss of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?(A) 0.80 mm (B) 0.70 mm (C) 0.50 mm (D) 0.75 mm
Answer» Answer is (A) 0.80 mm Main Scale Reading (MSR) = 0.5 mm Circular Scale Division (CSD) = 25^th Number of divisions on circular scale = 50 Pitch of screw = 0.5 mm ∴ LC of screw gauge = \(\frac{0.5} {50}\) = 0.01 mm ∴ zero error = -5 x LC = –0.05 mm ∴ zero correction = +0.05 mm Observed reading = 0.5 mm + (25 x 0.01) mm = 0.75 mm Corrected reading = 0.75 mm + 0.05 mm = 0.80 mm

65.

A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickenss of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?(A) 0.80 mm (B) 0.70 mm (C) 0.50 mm (D) 0.75 mm

Answer»

Answer is (A) 0.80 mm

Main Scale Reading (MSR) = 0.5 mm

Circular Scale Division (CSD) = 25^th

Number of divisions on circular scale = 50

Pitch of screw = 0.5 mm

∴ LC of screw gauge = \(\frac{0.5} {50}\) = 0.01 mm

∴ zero error = -5 x LC = –0.05 mm

∴ zero correction = +0.05 mm

Observed reading = 0.5 mm + (25 x 0.01) mm

= 0.75 mm

Corrected reading = 0.75 mm + 0.05 mm

= 0.80 mm

Discussion

66.	If `X=(a^(3)b^(2))/(sqrt(c)d)` and percentage errors in a, b, c and d are `1%, 2%, 4%` and `4%` respectively, then the error in X will beA. `10%`B. `11%`C. `13%`D. `5%`
Answer» Correct Answer - c `X=(a^(3)b^(2))/(sqrt(c)d)` `therefore` the relative error in X is `therefore (DeltaX)/(X)=3(Deltaa)/(a)+2(Deltab)/(b)+(1)/(2)(Deltac)/(c)+(Deltad)/(d)` (Errors are added) `therefore%` errors in the measurement of X will be `(DeltaX)/(X)xx100=3(Deltaa)/(a)xx100+2(Deltab)/(b)xx100` `+(1)/(2)(Deltac)/(c)xx100+(Deltad)/(d)xx100` `=3xx1%+2xx2%+(1)/(2)xx4%+4%` `=3%+4%+2%+4%=13%`

Discussion

67.	If p is the pitch of a screw then the distance by which the screw advances when given n rotations is `(p)/(n).`
Answer» Correct Answer - False

Discussion

68.	The percentage errors in the measurement of the length (L) and breadth (B) of a rectangle are 1% and b% respectively . Then the percentage error in the calculation of the area will be `"_______"`A. `(lb)%`B. `(1+b)%`C. `(L+1)(B+b)`D. `Lb+BL`
Answer» Correct Answer - B Errors are additive hence percentage error in area = `(a% + b%)`

Discussion

69.	`10^(6) mu `m are equal to one metre.
Answer» Correct Answer - True

Discussion

70.	If the percentage error in the measurement of length and breadth of a rectangle are 2% and 3% repectively then the percentage error in the determination of the area is 5%
Answer» Correct Answer - True

Discussion

71.	The error in the measurement of the diameter of a sphere is 2%. What is the percentage error in the measurement of its volume?A. `4%`B. `6%`C. `8%`D. `10%`
Answer» Correct Answer - b `V=(4)/(3)pir^(3)=(4)/(3)pi((d)/(2))^(3)=(4)/(3)pi(d^(3))/(8)=(1)/(6)pid^(3)` As `(1)/(6)` and `pi` are constants. `therefore (deltaV)/(V)xx100=3((deltad)/(d))xx100=3xx2%=6%`

Discussion

72.	A physical quantity X is given by `X=(2k^(3)l^(2))/(msqrt(n))` The percentage error in the measurement of K,l,m and n are 1%,2%, 3% and 4% respectively. The value of X is uncertain byA. 0.08B. 0.1C. 0.12D. None of these
Answer» Correct Answer - D A physical quantity `x=(2K^(3)l^(2))/(msqrtn)` Percentage error in `x=(3xx1+2xx2+3xx1+2xx(1)/(2))=11%`

Discussion

73.	While measuring the acceleration due to gravity by a simple pendulum, a student makes an error of 1% in the measurement of length and an error of 2% in the measurement of time. If he uses the formula for g as `g=4pi^(2)((L)/(T^(2)))`, then the percentage error in the measurement of g will beA. `3%`B. `4%`C. `5%`D. `6%`
Answer» Correct Answer - c `g=4pi^(2)((L)/(T^(2)))` `therefore (Deltag)/(g)=(DeltaL)/(L)+2(DeltaT)/(T)=(1)/(100)+(2xx2)/(100)=5%`

Discussion

74.	The distance between two points is measured as 2.784843 m. This is to be rounded off to 4 significant figures. Hence the value of the distance should be written asA. 2.784 mB. 2.785 mC. 2.7848 mD. 2.7849 m
Answer» Correct Answer - b As there should be four significant figures in the number 2.784843, the number of digits will be only four. Hence the distance will be 2.784m. We can omit the 6th and 7th numbers i.e. 4 and 3. But the fifth number is 8, which is greater than 5. Hence the fourth number 4, which is to be rounded off should be increased by one i.e. it should be 5. `therefore` The distance should be written as 2.785 m.

Discussion

75.	The error in the measurement of the radius of a sphere is 0.2%. What is the percentage error in the measurement of its surface area?A. `0.2%`B. `0.4%`C. `0.6%`D. `0.8%`
Answer» Correct Answer - b Given : `(Deltar)/(r)=0.2%` Area of a sphere `=4pir^(2)` There is no error in `4pi`, as it is a constant. `therefore (dA)/(A)=2(Deltar)/(r)=2xx0.2%=0.4%`

Discussion

76.	To calculate the volume of cylinder, a student is given a metre scale of least count 1 mm to measure its length and vernier callipers of least count 0.1 mm to measure its diameter. If its length and radius are 10 cm and 2 cm respectively then the percentage error in the calculated value of the volume of the cylinder will beA. `5%`B. `4%`C. `3%`D. `2%`
Answer» Correct Answer - d Volume of a cyclinder `V=pir^(2)L` L.C. of metre scale = 0.1 cm and L.C. of vernier = 0.01 cm and `DeltaL=0.1cm, Deltar=0.01cm` `therefore` Percentage error = `(DeltaV)/(V)xx100` `=[2(Deltar)/(r)+(DeltaL)/(L)]xx100` `=[2xx(0.01)/(2)+(0.01)/(10)]xx100` `=[2xx(0.01)/(2)+(0.1)/(10)]xx100` `=[(1)/(100)+(1)/(100)]xx100=2%`

Discussion

77.	For each of the two vernier callipers P and Q, 1 MSD = 1mm. For P, 10 VSD = 8 MSD and for Q, 20 VSD = 15 MSD. The vernier callipers that gives more accurate reading is ____________.A. PB. QC. Both P and Q give equal accurancy.D. Data insufficient.
Answer» Correct Answer - A For P and Q 1 MSD = 1mm For P 10 VSD = 8 MSD = 8 mm 1 VSD = 0.8 mm ` L.C = 1 MSD- 1 VSD = = 1-0.8= 0.2 mm` `"For" Q 20 VSD = 15 MDS = 15mm` ltBrgt 1 VSD = 0.75 mm L.C = 1 MSD - 1 VSD = 1 - 0.75 = 0.25 mm L.c. of is less than Q. Therefore, the reading of P is more accurate than Q.

Discussion

78.	The least count of a vernier callipers P and Q, 1 MSD = 1 mm. For P, 10 VSD + 8 MSD and for Q, 20 VSD = 15 MSD. The vernier callipers that gives more accurate reading is _______________.A. 0..1 mmB. 0.01 cmC. 0.1 cmD. 0.001 mm
Answer» Correct Answer - B 10 VSD = 9 mm 1 VSD = 0.9 mm 1 MSD = 1 mm Least count = 1 MSD - 1 VSD = 1 mm - 0.9 mm = 0.1 mm = 0.01 cm

Discussion

79.	A stock of identical coins are placed on a scale as shown in the figure. The thickness of a coin is `"_______"` A. (a) 1.8 cmB. (b)18 mmC. (c ) 1.8 mmD. (d) 0.18 m
Answer» Correct Answer - C Number of coins = 10 Total length = 2.4 -0.6 = 1.8 cm = 18 mm Thickness of one coin=`18/10=1.8 " mm "`

Discussion

80.	A stock of identical coins are placed on a scale as shown in the figure. The thickness of a coin is `"_______"` A. (a) 1.8 cmB. (b) 18 mmC. ( c) 1.8D. (d) 0.18 m
Answer» Correct Answer - C Number of coins = 10. Total length = 2.4 - 0.6 = 1.8 cm = 18 mm. Thickness of one coin = 18/10 = 1.8 mm.

Discussion

81.	A pile of identical one rupee coins are placed over a metre scale as shown in the figure. The thickness of a one rupee coin is_____ A. 1.56 mmB. 1.56 cmC. 1.67 mmD. 1.67 cm
Answer» Correct Answer - A

Discussion

82.	`{:(,"Column A",,"Column B"),("(A)","Measuring cylinder","(a)","kgf, gf"),("(B)","Gavitational units of weight","(b)","ml of cc"),("(C)","1 g "cm^(-3) ,"(c)","Zero weight"),("(D)","Zero gravitational force","(d)",1000" kg "m^(-3)):}`A. (a)` Atob, Btoa, Ctod, Dtoc.` (b) `Atob,Btod, Ctoa, Dtoc,` (c ) `Atoc,Btod, Ctob,Dtoa` (d) `Atoa, Btoc,Ctob, Dtod`B.C.D.
Answer» Correct Answer - A A-b " "A measuring cylinder is used to measure the volume of liquids in millitres or cubic centimetres. B-a " "Gravitational units of weight are kgf and gf. ,brgt C-d " "The units of density are " g " `cm^(-3)` , " kg " `m^(-3)` They are related are " g " `cm^(-3)` = 1000 " kg " `m^(-3)` ,brgt D-c " " If the gravitational force acting on a body is zero, then the weight of the body is said to be zero.

Discussion

83.	The mass of a body of weight 200 gf is _____g.A. 200B. 300C. 400D. 20
Answer» Correct Answer - A

Discussion

84.	The weight of a body on the earth is 500 gf. The volume of water displaced when it is immersed in water in` 250 ""cm^(3)`. Determine the density of the material fo the body.
Answer» Density = `"mass"/"volume"` Mass of the body = `500 " g "` (`:.` mass of a body of weight 1 gf = 1 g ) Volume of the body = volume of water displaced = 250 `cm^(3)` Density = `500/250= 2 " g "cm^(-3)`

Discussion

85.	A student took a spring balance calibrated in gf. He then suspended an object of mass 1 kg to the spring balance. Determine what would be the reading of the spring balance.
Answer» Weight of 1 kg body = 1 kgf =`1 xx 10^(3) " gf " =10^(3) " gf "` The reading on the spring balance is 1000 gf.

Discussion

86.	The fundamental unit of time viz. the second, is based upon the vibrations of the atoms of the following element.A. KryptonB. XenonC. CesiumD. Lithium
Answer» Correct Answer - c

Discussion

87.	Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon the velocity `upsilon,` of water, its density `rho` and acceleration due to gravity g, then m is directly proportional toA. `v^(3)`B. `v^(4)`C. `v^(5)`D. `v^(6)`
Answer» Correct Answer - D `mpropv^(a)p^(b)g^(c)`. Writing the dimensions on both sides `[M]=[LT^(-1)]^(a)[ML^(-3)][LT^(-2)]^(c)` `[M]=[M^(b)L^(a)-^(3b+c)T^(-a-2c)]` `:. b=1` `a-3b+c=0implies-a-2c=0`Solving these, we get `a=6 ` Hence, `mpropv^(6)`

Discussion

88.	C and R denote the capacitance and resistance respectively. What is the dimensional formula of CR?A. `[M^(0)L^(0)T^(0)]`B. `[M^(0)L^(0)T^(1)]`C. `[M^(0)L^(0)T^(-1)]`D. `[M^(1)L^(0)T^(-1)]`
Answer» Correct Answer - b `C=(Q)/(V)andR=(V)/(I)` `therefore CR=(Q)/(V)xx(V)/(I)=(Q)/(I)=(Ixxt)/(I)=t` `therefore [CR]=[T^(1)]=[M^(0)L^(0)T^(1)]`

Discussion

89.	The wavelength of a spectral line is 480 nm. What is its value in mn?A. `480xx10^(-7)mm`B. `48xx10^(-5)mm`C. `48xx10^(-6)mm`D. `4.8xx10^(-5)mm`
Answer» Correct Answer - b `480nm=480xx10^(-9)m=480xx10^(-9)xx10^(3)mm` `=48xx10^(-5)mm`

Discussion

90.	The distance between two cities A ad B in a map is 7.5 cm. the scale taken for drawing this map is 1cm=1,50,000m. The actual distance between A and B is____km.A. 1125000B. 20000C. 200D. 1125
Answer» Correct Answer - D

Discussion

91.	Which of the following pair has same dimensions? (A) Current density and charge density (B) Angular momentum and momentum (C) Spring constant and surface energy (D) Force and torque
Answer» Answer is (C) Spring constant and surface energy

Discussion

92.	The periodic time (T) of a simple pendulum of length (L) is given by `T=2pisqrt((L)/(g))`. What is the dimensional formula of `Tsqrt((g)/(L))`?A. `[M^(0)L^(1)T^(0)]`B. `[M^(0)L^(0)T^(0)]`C. `[M^(1)L^(1)T^(-1)]`D. `[M^(0)L^(-1)T^(1)]`
Answer» Correct Answer - b `because T=2pisqrt((L)/(g)) therefore (T)/(sqrt((L)/(g)))=Tsqrt((g)/(L))=2pi` But `2pi` is a constant and it has the dimensions of `M^(0)L^(0)T^(0)` `therefore` The dimensional formula for `Tsqrt((g)/(L))` is `[M^(0)L^(0)T^(0)]`

Discussion

93.	What is the dimensional formula of the term `(a)/(b)` in the equation `P=((a+x)/(b))`, where P is the pressure and x is the distance?A. `[M^(1)L^(-1)T^(2)]`B. `[ML^(-1)T^(-2)]`C. `[M^(1)L^(2)T^(-1)]`D. `[M^(-1)L^(-2)T^(1)]`
Answer» Correct Answer - b `P=(a+x)/(b)=(a)/(b)+(x)/(b)` `therefore` Dimensions of P = Dimension of `(a)/(b)` `therefore [(a)/(b)]=[P]=[(F)/(A)]=[(M^(1)L^(1)T^(-2))/(L^(2))]=[M^(1)L^(-1)T^(-2)]`

Discussion

94.	Which of the following is not the unit of energy?(A) watt-hour (B) electron volt (C) N m (D) kgm2s-2
Answer» Answer is (C) N m

Discussion

95.	Show that the expression of the time period T of a simple pendulum of length l given by `T = 2pi sqrt((l)/(g))` is dimensionally correctA. RightB. WrongC. Information incompleteD. None of these
Answer» Correct Answer - A Give, `T=2pisqrt(l)/(g)` Dimensionally `[T]=sqrt(([L])/([LT^(-2)]))=[T]` As in the above equation, the dimensions of both side are same. Therefore, the given formula is dimensionally correct.

Discussion

96.	The dimensional formula for the ratio of angular to linear momentum isA. `[M^(1)L^(1)T^(0)]`B. `[M^(0)L^(1)T^(0)]`C. `[M^(0)L^(2)T^(1)]`D. `[M^(1)L^(2)T^(0)]`
Answer» Correct Answer - b Angular momentum (L) = `Iomega=mr^(2)xx(v)/(r)=mvr` and Linear momentum (P) = mv `therefore (L)/(P)=(mvr)/(mv)=r` `therefore [(L)/(P)]=[M^(0)L^(1)T^(0)]`

Discussion

97.	In the following dimensionally correct equation `F=(X)/("Linear Density")`, where F is the force. What is the dimensional formula for X?A. `M^(0)L^(0)T^(0)`B. `M L T^(-2)`C. `M^(2)L^(-2)T^(-2)`D. `M^(2)L^(0)T^(-2)`
Answer» Correct Answer - d By using the principle of homogeneity of dimensions, `\|F\|=\|(X)/("Linear density")\|" ... (1)"` But linear density = mass per unit length `therefore` [Linear density] `=[(M)/(L)]=[M^(1)L^(-1)]" ... from (1)"` `therefore [L^(1)M^(1)T^(-2)]=[(X)/(M^(1)L^(-1))]` `therefore [X]=[M^(2)L^(0)T^(-2)]`

Discussion

98.	Dimension of surface tension is(A) [M1 L2 T2] (B) [M1 L0 T-2] (C) [M1 L2 T-2] (D) [M0 L0 T-2]
Answer» Answer is (B) [M¹ L⁰ T^-2]

Discussion

99.	Dimension of force constant is given by(A) [M1L1T–2] (B) [M0L1 T–1] (C) [M1 L0 T–2] (D) [M1 L0 T–1]
Answer» Answer is (C) [M¹L⁰T^–2]

Discussion

100.	What are the dimensional formulae of `omega` and K in the relation `y=Asin(omegat-Kx)`?A. `[M^(0)L^(0)T^(2)][M^(0)L^(-1)T^(0)]`B. `[M^(0)L^(0)T^(-1)][M^(0)L^(-1)T^(0)]`C. `[M^(0)L^(0)T^(-1)][M^(0)L^(1)T^(0)]`D. `[M^(0)L^(0)T^(-1)][M^(0)L^(1)T^(-1)]`
Answer» Correct Answer - b The argument of any trignometrical function is an angle. `therefore (omegat-Kx)` is an angle `(theta)`. It has no dimensions. `therefore omegat` and Kx are dimensionless. `omegat` is dimensionless, if the dimension of `omega` `=(1)/(T)=T^(-1)` `therefore [omega]=[M^(0)L^(0)T^(-1)]` Similarly, Kx will be dimensionless, if the dimension of `K=(1)/(x)=(1)/(L)=L^(-1)` `therefore [K]=[M^(0)L^(-1)T^(0)]`

Discussion

Explore topic-wise InterviewSolutions in .

What is the dimensional formula for pressure gradient?A. `[M^(1)L^(2)T^(-1)]`B. `[M L^(-2)T^(-2)]`C. `[M^(-2)L^(-2)T^(0)]`D. `[M^(0)L^(2)T^(-2)]`

Which one of the following gives the dimensional formula of coefficient of friction?A. `[M LT^(-2)]`B. `[M^(2)LT^(-2)]`C. `[M^(0)L^(0)T^(0)]`D. `[M^(2)LT]`

Which one of the following gives the dimensional formula of coefficient of friction?A. `[MLT^(-2)]`B. `[M^(2)LT^(-2)]`C. `[M^(0)L^(0)T^(0)]`D. `[M^(2)LT]`

What is the dimensional formula of specific resistance in terms of charge Q?A. `M^(1)L^(2)T^(-2)Q^(-1)`B. `M^(1)L^(2)T^(-2)Q^(-2)`C. `M^(1)L^(3)T^(-1)Q^(-2)`D. `M^(1)L T^(-2)Q^(-1)`

Given the specific gravity of gold as 19 the mass of 100 cm volume of gold is `"______"` kg

S.I. unit of specific resistance is(A) Ω cm (B) Ω m (C) Ω/cm (D) mho-cm

S. I unit of principle specific heat is(A) kcal/gm K (B) cal/gm K (C) J/kg K (D) erg/kg K

The S.I. units of the constant in Wein’s displacement law are(A) cm K-1 (B) mK (C) cm2 K-1 (D) cm K-2

The error in the measurement of length (L) of the simple pendulum is 0.1% and the error in time period (T) is 3%. The maximum possible error in the measurement of \(\frac{L}{T^2}\) is(A) 2.9% (B) 3.1% (C) 5.9% (D) 6.1%

The error in the measurement of the radius of a sphere is `1%`. Find the error in the measurement of volume.A. `1%`B. `2%`C. `3%`D. `5%`

The base of the parallelogram is 16 cm and the height is 7 cm less than its base. Find the area of the parallelogram.

The dimensions of `1/2 in_(0) E^(2)` (`in_(0)`: permittivity of free space, E: electric field) is-A. `[ML^(2)T^(-1)]`B. `[ML^(-1)T^(-2)]`C. `[ML^(2)T^(-2)]`D. `[MLT^(-1)]`

A student uses a metre scale, measuring upto 1 mm, to measure the length and breadth of a rectangular plate. He finds that length = 5.7 cm and breadth = 3.4 cm. What is the percentage error in the area of the plate ?A. `3.5%`B. `4.7%`C. `5.3%`D. `6.2%`

If `X=(a^(3)b^(2))/(sqrt(c)d)` and percentage errors in a, b, c and d are `1%, 2%, 4%` and `4%` respectively, then the error in X will beA. `10%`B. `11%`C. `13%`D. `5%`

If p is the pitch of a screw then the distance by which the screw advances when given n rotations is `(p)/(n).`

The percentage errors in the measurement of the length (L) and breadth (B) of a rectangle are 1% and b% respectively . Then the percentage error in the calculation of the area will be `"_______"`A. `(lb)%`B. `(1+b)%`C. `(L+1)(B+b)`D. `Lb+BL`

`10^(6) mu `m are equal to one metre.

If the percentage error in the measurement of length and breadth of a rectangle are 2% and 3% repectively then the percentage error in the determination of the area is 5%

The error in the measurement of the diameter of a sphere is 2%. What is the percentage error in the measurement of its volume?A. `4%`B. `6%`C. `8%`D. `10%`

A physical quantity X is given by `X=(2k^(3)l^(2))/(msqrt(n))` The percentage error in the measurement of K,l,m and n are 1%,2%, 3% and 4% respectively. The value of X is uncertain byA. 0.08B. 0.1C. 0.12D. None of these

The distance between two points is measured as 2.784843 m. This is to be rounded off to 4 significant figures. Hence the value of the distance should be written asA. 2.784 mB. 2.785 mC. 2.7848 mD. 2.7849 m

The error in the measurement of the radius of a sphere is 0.2%. What is the percentage error in the measurement of its surface area?A. `0.2%`B. `0.4%`C. `0.6%`D. `0.8%`

For each of the two vernier callipers P and Q, 1 MSD = 1mm. For P, 10 VSD = 8 MSD and for Q, 20 VSD = 15 MSD. The vernier callipers that gives more accurate reading is ____________.A. PB. QC. Both P and Q give equal accurancy.D. Data insufficient.

The least count of a vernier callipers P and Q, 1 MSD = 1 mm. For P, 10 VSD + 8 MSD and for Q, 20 VSD = 15 MSD. The vernier callipers that gives more accurate reading is _______________.A. 0..1 mmB. 0.01 cmC. 0.1 cmD. 0.001 mm

A stock of identical coins are placed on a scale as shown in the figure. The thickness of a coin is `"_______"` A. (a) 1.8 cmB. (b)18 mmC. (c ) 1.8 mmD. (d) 0.18 m

A stock of identical coins are placed on a scale as shown in the figure. The thickness of a coin is `"_______"` A. (a) 1.8 cmB. (b) 18 mmC. ( c) 1.8D. (d) 0.18 m

A pile of identical one rupee coins are placed over a metre scale as shown in the figure. The thickness of a one rupee coin is_____ A. 1.56 mmB. 1.56 cmC. 1.67 mmD. 1.67 cm

The mass of a body of weight 200 gf is _____g.A. 200B. 300C. 400D. 20

The weight of a body on the earth is 500 gf. The volume of water displaced when it is immersed in water in` 250 ""cm^(3)`. Determine the density of the material fo the body.

A student took a spring balance calibrated in gf. He then suspended an object of mass 1 kg to the spring balance. Determine what would be the reading of the spring balance.

The fundamental unit of time viz. the second, is based upon the vibrations of the atoms of the following element.A. KryptonB. XenonC. CesiumD. Lithium

Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon the velocity `upsilon,` of water, its density `rho` and acceleration due to gravity g, then m is directly proportional toA. `v^(3)`B. `v^(4)`C. `v^(5)`D. `v^(6)`

C and R denote the capacitance and resistance respectively. What is the dimensional formula of CR?A. `[M^(0)L^(0)T^(0)]`B. `[M^(0)L^(0)T^(1)]`C. `[M^(0)L^(0)T^(-1)]`D. `[M^(1)L^(0)T^(-1)]`

The wavelength of a spectral line is 480 nm. What is its value in mn?A. `480xx10^(-7)mm`B. `48xx10^(-5)mm`C. `48xx10^(-6)mm`D. `4.8xx10^(-5)mm`

The distance between two cities A ad B in a map is 7.5 cm. the scale taken for drawing this map is 1cm=1,50,000m. The actual distance between A and B is____km.A. 1125000B. 20000C. 200D. 1125

Which of the following pair has same dimensions? (A) Current density and charge density (B) Angular momentum and momentum (C) Spring constant and surface energy (D) Force and torque

The periodic time (T) of a simple pendulum of length (L) is given by `T=2pisqrt((L)/(g))`. What is the dimensional formula of `Tsqrt((g)/(L))`?A. `[M^(0)L^(1)T^(0)]`B. `[M^(0)L^(0)T^(0)]`C. `[M^(1)L^(1)T^(-1)]`D. `[M^(0)L^(-1)T^(1)]`

What is the dimensional formula of the term `(a)/(b)` in the equation `P=((a+x)/(b))`, where P is the pressure and x is the distance?A. `[M^(1)L^(-1)T^(2)]`B. `[ML^(-1)T^(-2)]`C. `[M^(1)L^(2)T^(-1)]`D. `[M^(-1)L^(-2)T^(1)]`

Which of the following is not the unit of energy?(A) watt-hour (B) electron volt (C) N m (D) kgm2s-2

Show that the expression of the time period T of a simple pendulum of length l given by `T = 2pi sqrt((l)/(g))` is dimensionally correctA. RightB. WrongC. Information incompleteD. None of these

The dimensional formula for the ratio of angular to linear momentum isA. `[M^(1)L^(1)T^(0)]`B. `[M^(0)L^(1)T^(0)]`C. `[M^(0)L^(2)T^(1)]`D. `[M^(1)L^(2)T^(0)]`

In the following dimensionally correct equation `F=(X)/("Linear Density")`, where F is the force. What is the dimensional formula for X?A. `M^(0)L^(0)T^(0)`B. `M L T^(-2)`C. `M^(2)L^(-2)T^(-2)`D. `M^(2)L^(0)T^(-2)`

Dimension of surface tension is(A) [M1 L2 T2] (B) [M1 L0 T-2] (C) [M1 L2 T-2] (D) [M0 L0 T-2]

Dimension of force constant is given by(A) [M1L1T–2] (B) [M0L1 T–1] (C) [M1 L0 T–2] (D) [M1 L0 T–1]

What are the dimensional formulae of `omega` and K in the relation `y=Asin(omegat-Kx)`?A. `[M^(0)L^(0)T^(2)][M^(0)L^(-1)T^(0)]`B. `[M^(0)L^(0)T^(-1)][M^(0)L^(-1)T^(0)]`C. `[M^(0)L^(0)T^(-1)][M^(0)L^(1)T^(0)]`D. `[M^(0)L^(0)T^(-1)][M^(0)L^(1)T^(-1)]`