399 + Interview Questions in UNITS-AND-MEASUREMENTS IN GENERAL AWARENESS Page 2 InterviewSolution

51.	The solid angle subtended by the periphery of an area `1cm^(2)` at a point situtated symmetrically at a distance of 5 cm from the area isA. `2xx10^(-2)` steradianB. `4xx10^(-2)` steradianC. `6xx10^(-2)` steradianD. `8xx10^(-2)` steradian
Answer» Correct Answer - B Solid angle `dOmega=(dA)/(r^(2))=(1cm^(2))/((5cm)^(2))` `=4xx10^(-2)` Steradian

Discussion

52.	A drop of olive oil of radius 0.25 mm spreads into a circular film of radius 5 cm on the water surface. Estimate the molecular size of the olive oil
Answer» Area of the film, `A=pir^2cm^2` `=25 pi cm^2` [`because` Radius of the film, r=5cm] Volume of the drop, V=`4/3pi "(Radius of oil drop)"^3` `=4/3xxpixx(0.25 mm)^3` `=4/3xxpixx(2.5xx10^(-1))^3 mm^3` `=4/3xxpixx15.6xx10^(-3)mm^3` `=4/3xxpixx15.6xx10^(-6) cm^3` Molecular size = Thickness of the film `=V/A` `=(4pixx15.6xx10^(-6))/(3xx25pi)` `=0.83xx10^(-6)` cm `=8.3xx10^(-9)` m

Discussion

53.	If the average life of a person is taken as 100 s the age of the universe on this scale is of the orderA. `10^(10)s`B. `10^(8)s`C. `10^(17)s`D. `10^(9)s`
Answer» Correct Answer - A

Discussion

54.	10 drops of an oleic acid solution of concentration `1/400 cm^3` per `cm^3` of alcohol, are dropped on a water surface. The circular film thus produced has radius 10 cm. Find the molecular size of oleic acid, if the radius of each drop is 1.4 mm.
Answer» `t="nV"/"400A"` or `9.15xx10^(-9)` m

Discussion

55.	If a human heart beats once in every 0.8 s, find the number of times it has beaten in the life of a 10 year old boy
Answer» Number of seconds in 10 years =365.25 x 10 x 86400 Number of times the human heart beats in 10 years.=`(365.25xx864000)/0.8` or `3.94xx10^8` times

Discussion

56.	Which of the following physical quantities has same unit in all the three system of units?A. massB. lenthC. timeD. none of these
Answer» Correct Answer - C Unit of time (i.e., second) is same in all the three system of units.

Discussion

57.	You measure two quantities as `A=1.0m+-0.2m`,`B=2.0m+-0.2m`. We should report correct value for `sqrt(AB)` asA. `1.4m+-0.4m`B. `1.41m+-0.15m`C. `1.4m+-0.3m`D. `1.4m+-0.2m`
Answer» Correct Answer - D Here, `A=1.0+-0.2m,B=2.0m+-0.2m` `AB=(1.0m)(2.0m)=2.0m^(2)` `sqrt(AB)=sqrt(2.0)m=1.414m` Rounding off to two significant figures, we get `sqrt(AB)=1.4m` `(Deltasqrt(AB))/(sqrt(AB))=(1)/(2)((DeltaA)/(A)+(DeltaB)/(B))=(1)/(2)((0.2)/(1.0)+(0.2)/(2.0))=(0.3)/(2)` `Deltasqrt(AB)=(0.3)/(2)xxsqrt(AB)=(0.3)/(2)xx1.414=0.212m` Rounding off to one significant figures, we get `Deltasqrt(AB)=0.2m` The correct value for `sqrt(AB)` is `1.4m+-0.2m`

Discussion

58.	You measure two quantities as `A=1.0m+-0.2m`,`B=2.0m+-0.2m`. We should report correct value for `sqrt(AB)` asA. `1.4m+-0.4m`B. `1.41m+-0.15m`C. `1.4m +-0.3 m`D. `1.4 m+-0.2m`
Answer» Correct Answer - D `"Given"," "A=1.0m+-0.2m, B=2.0m+-0.2m` `"Let"," "Y=sqrt(AB)=sqrt((1.0)(2.0))=1.414 m ` Rounding off to two significant digit Y=1.4m `(DeltaY)/Y=1/2[(DeltaA)/A+(DeltaB)/B]=1/2[(0.2)/(1.0)+(0.2)/(2.0)]=(0.6)/(2xx2.0)` `Rightarrow " "DeltaY=(0.6Y)/(2xx2.0)=(0.6xx1.4)/(2xx2.0)=0.212` Rounding off to one significant digit `DeltaY==0.2m` Thus, correct value for `sqrt(AB)=r+Deltar=1.4+-0.2m`

Discussion

59.	STATEMENT-1 A dimensionless quantity may have a unit STATEMENT-2 A constant may not be unitless.A. Statement-1 is True , Statement-2 is True ,Statement-2 is a correct explanation for Statement-1B. Statement-1 is True , Statement-2 is True ,Statement-2 is NOT a correct explanation for Statement-1C. Statement-1 is True , Statement-2 is FalseD. Statement-1 is False, Statement-2 is True
Answer» Correct Answer - 2

Discussion

60.	The following is a unitless and dimensionless quantityA. AngleB. Solid angleC. Mechanical equivalent of heatD. Coefficient of friction
Answer» Correct Answer - D

Discussion

61.	A dimensionless quantity y is represented by the formula `y=(a-bc)/(d+e)`. Which of following is/arecorrect?A. Dimensions of d and e are sameB. abc and de have same dimensionsC. `"bc"/"ae+d"` is dimensionlessD. de+dc is not meaningful
Answer» Correct Answer - 1,2,4

Discussion

62.	Let `y=A sin (omegat-kx)` represent the variation of distance y of a particle with time t. Which of the following is not meaningful?A. `y/A+omega`B. `y/omega+"At"/"kx"`C. A-kxD. `A+omega/k`
Answer» Correct Answer - 1,3,4

Discussion

63.	The displacement of a progressive wave is represented by `y = A sin (omegat - kx),` where x is distance and t is time. Write the dimensional formula of (i) `omega` and (ii) k.
Answer» Now, by the principle of homogeneity, i.e., dimensions of LHS and RHS should be equal, `"hence "" "[LHS]=[RHS]` `Rightarrow [L]=[A]=L` `"As "omegat-kx" should be dimensionless",[omegat]=[kx]=1` `Rightarrow [omega]T=[k]L=1` `Rightarrow [omega]=T^(-1) and [k]L=1^(-1)`

Discussion

64.	Time for 20 oscillations of a pendulum is measured as `t_1 = 39.6 s , t_2 = 39.9 s , t_3 = 39.5.` What is the precision in the measurements ? What is the accuracy of the measurement ?
Answer» `"Given"," "t_(1)=39.6s,t_(2)=39.9 s and t_(3)=39.5 s` Least count of measuring instrument=`0.1 s` (As measurements have only one decimal place) Precision in the measurment = Least count of the measuring instrument =`0.1 s` Mean value of time for 20 oscillations is given by `t=(t_(1)+t_(2)+t_(3))/3` `=(39.6+39.9+39.5)/3=39.7 s ` Absolute errors in the measurements `Deltat_(1)=t-t_(1)=39.7-39.6=0.1 s` `Deltat_(2)=t-t_(2)=39.7-39.9=-0.2 s` `Deltat_(3)=t-t_(3)=39.7-39.5=0.2 s` `"Mean absolute error "=(\|Deltat_(1)\|+\|Deltat_(2)\|+\|Deltat_(3)\|)/3` `=(0.1+0.2+0.2)/3` `=(0.5)/3=0.17approx0.2" ""(rounding off upto one decimal place)"` `therefore" Accuracy of measurement "=+-0.2 s`

Discussion

65.	A physical performs an experiment and taken 200 readings. He repeats the same experiment and now takes 800 readingbs. By doing soA. the probable error remains sameB. the probable error is four timesC. the probable error is halvedD. the probable error si reduced by a factor `¼`
Answer» Correct Answer - D

Discussion

66.	The erros that always occur in the measurement with screw gauge isA. random errorsB. systematic errorsC. gross errorsD. neglibible errors
Answer» Correct Answer - B

Discussion

67.	If in a Vernier callipers 10 VSD coincides with 8 MSD, then the least count of Vernier calliper is [given 1 MSD = 1mm]A. `1xx10^(-4)m`B. `2xx10^(-4)m`C. `1xx10^(-3)m`D. `8xx10^(-4)m`
Answer» Correct Answer - B

Discussion

68.	Dimension of resistance in an elecatrical circuit, in terms of dimension of mass `M`, of length `L`, of time `T`, and of current `I`, would beA. `[ML^(2)T^(-3)I^(-2)]`B. `[ML^(2)T^(-3)I^(-1)]`C. `[ML^(2)T^(-2)]`D. `[ML^(2)T^(-1)I^(-1)]`
Answer» Correct Answer - A

Discussion

69.	A student measures that distance traversed in free fall of a body, initially at rest in given time. He uses this data to estimated `g`, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are `e_(1)` and `e_(2)`, respectively, the percentage error in the estimation of `g` isA. `e_(2)-e_(1)`B. `e_(1)+2e_(2)`C. `e_(1)+e_(2)`D. `e_(1)-2e_(2)`
Answer» Correct Answer - B

Discussion

70.	STATEMENT 1 The final result obtained after a number of calculations is rounded off to a proper number of significant figures. STATEMENT 2. No final result can have more accuracy than the original data from which it was derivedA. Statement-1 is True , Statement-2 is True ,Statement-2 is a correct explanation for Statement-1B. Statement-1 is True , Statement-2 is True ,Statement-2 is NOT a correct explanation for Statement-1C. Statement-1 is True , Statement-2 is FalseD. Statement-1 is False, Statement-2 is True
Answer» Correct Answer - 1

Discussion

71.	The figure shows a wall clock hanging on a wall it only has the hour hand STATEMENT:1-The least count of the clock is 12 minutes. STATEMENT:2-The observer reads 2hrs 12 minutes AM/PMA. Statement-1 is True , Statement-2 is True ,Statement-2 is a correct explanation for Statement-1B. Statement-1 is True , Statement-2 is True ,Statement-2 is NOT a correct explanation for Statement-1C. Statement-1 is True , Statement-2 is FalseD. Statement-1 is False, Statement-2 is True
Answer» Correct Answer - 2

Discussion

72.	In Column-I, some physical quantities are given and in column-II, dimensions of the physical quantities are given . Match the entries in column-I to each entry in Column-II.
Answer» Correct Answer - A(r) ; B(r); C(q) ;D(q)

Discussion

73.	match the following
Answer» Correct Answer - A(r); B(s) ;C(q); D(p)

Discussion

74.	If the unit of force is 1 kN, unit of length 1 km and unit of time is 100s, what will be the unit of mass?A. 1000 kgB. 1 kgC. 10000 kgD. 100 kg
Answer» Correct Answer - C

Discussion

75.	The dimension of magnetic field in `M,L,T and C` (coulomb) is given as
Answer» From `F = Bqv` `B = (F)/(qv) = ([MLT^(-2)])/(C[LT^(-1)]) = [M^(1) L^(0) T^(-1) C^(-1)]`

Discussion

76.	The respective number of signficant figures for the numbers `23.023, 0.0003 and 2.1 xx 10^(-3)` are
Answer» (i) All non-zero numbers are significant figurers. Zeores occuring between zero digits are also significant. (ii) If the numbers is less than one, zero between the decimal and first non zero digit are not significant. (iii) Powers of `10` is not a significant figure. `:. 5,1,2`

Discussion

77.	A stick has a length of `12.132cm` and an other stick has a length of `12.4cm` then the total length of the stick is...........A. `24.53cm`B. `24.5 cm`C. `2.overline(45) cm`D. `2.453cm`
Answer» Correct Answer - B

Discussion

78.	The number of significiant figures in `5.69 xx 10^(15) kg` isA. `1`B. `2`C. `3`D. `4`
Answer» Correct Answer - C

Discussion

79.	How many light years alpha centauri away from the earth?A. 1.29B. 2.29C. 3.29D. 4.29
Answer» Correct Answer - D Alpha centauri is 4.29 light years away from the earth.

Discussion

80.	Which of the following pairs of physical quantities have same dimensions?A. Force and powerB. Torque and energyC. Torque and powerD. Force ad torque.
Answer» Correct Answer - B b

Discussion

81.	A dimensionless quantityA. never has a unitB. always has unitC. may have a unitD. does not exit
Answer» Correct Answer - C c

Discussion

82.	Assertion: The dimensional formula of surface energy is `[M^(1)L^(2)T^(-2)]`. ltBrgt Reason: Surface energy has same dimensions as that of potential energy.A. if both assertion and reason are true reason is the correct explanation of assertion.B. If both assertion and reason are true but reason is not the correct explanation fo assertion.C. If assertion is true but reaso is false.D. IF both assertion and reason are false.
Answer» Correct Answer - B Dimensional formula of surface energy is `[ML^(2)T^(-2)]`

Discussion

83.	Assertion: Force can be added to pressure. Reason: Force and pressure have same dimensions.A. if both assertion and reason are true reason is the correct explanation of assertion.B. If both assertion and reason are true but reason is not the correct explanation fo assertion.C. If assertion is true but reaso is false.D. IF both assertion and reason are false.
Answer» Correct Answer - D The dimensions of force is `[M^(1)L^(1)T^(-2)]`. Dimensions of pressure is `[M^(1)L^(-1)T^(-2)]`. Quantities with different dimension can not be added.

Discussion

84.	Light year is a unit ofA. DistanceB. timeC. speedD. intensity of light
Answer» Correct Answer - A 1 light year=9.46xx10^(15)m` (Distance travelled by light in 1 year)

Discussion

85.	Which one of the following methods is used to measure distance of a planet or a star from the earth?A. Echo methodB. Parallax methodC. Triangulation methodD. none of these
Answer» Correct Answer - B b

Discussion

86.	In the relation P=`alpha/beta , e^((alphax)/(nR theta))` , P is power , x is distance n is number of moles, R is gas constant and `theta` is temperature dimensional formula of `beta` isA. `[M^0L^0T^0]`B. `[M^(-1)L^0T^1]`C. `[M^0L^(-1)T^1]`D. `[M^0L^(-1)T^(-1)]`
Answer» Correct Answer - 3

Discussion

87.	A student performs exeriment with simple pendulum and measures time for `10` vibrations. If the measures the time for `100` vibrations, the error in measurement of time period will be reduced by a factor of......A. `10`B. `90`C. `100`D. `1 overline(0)00`
Answer» Correct Answer - A `(X_(1))/(X_(2)) = (N_(2))/(N_(1))`

Discussion

88.	The frequency `f` of vibrations of a mass `m` suspended from a spring of spring constant `k` is given by `f = Cm^(x) k^(y)` , where `C` is a dimensionnless constant. The values of `x and y` are, respectively,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`
Answer» Correct Answer - 4

Discussion

89.	The frequency `f` of vibrations of a mass `m` suspended from a spring of spring constant `k` is given by `f = Cm^(x) k^(y)` , where `C` is a dimensionnless constant. The values of `x and y` are, respectively,A. `(1)/(2),(1)/(2)`B. `-(1)/(2),-(1)/(2)`C. `(1)/(2),-(1)/(2)`D. `-(1)/(2),(1)/(2)`
Answer» `f = (1)/(2pi) sqrt((k)/(m))`

Discussion

90.	If `L, R , C , and V`, respectively , represent inductance , resistance , capacitance and potential difference , then the dimensions of `L //RCV` are the same as those ofA. ChargeB. `1//"Charge"`C. CurrentD. `1//"Current"`
Answer» Correct Answer - D `(L)/(RCV) = (L)/(t (L. (dt)/(dt)))`

Discussion

91.	The length of a rod is measured as `35.3cm` then the gradutions ont eh scale are up toA. `1cm`B. `1mm`C. `0.01mm`D. `0.1mm`
Answer» Correct Answer - D `0.01cm` is the `L.C` of vernier caliperse.

Discussion

92.	Assertion: The given equation `x = x_(0) + u_(0)t + (1)/(2) at^(2)` is dimensionsally correct, where x is the distance travelled by a particle in time t , initial position `x_(0) ` initial velocity `u_(0)` and uniform acceleration a is along the direction of motion. Reason: Dimensional analysis can be used for cheking the dimensional consistency or homogenetly of the equation.A. if both assertion and reason are true reason is the correct explanation of assertion.B. If both assertion and reason are true but reason is not the correct explanation fo assertion.C. If assertion is true but reaso is false.D. IF both assertion and reason are false.
Answer» Correct Answer - A Given equation `x=x_(0)+u_(0)t+(1)/(2)at^(2)`. The dimensions of each term may be written as `[x]=[L],[x_(0)]=[L],[u_(0)t]=[LT^(-1)][T]=[L]` `[((1)/(2))at^(2)]=[LT^(-2)][T^(2)]=[L]` As each ter on the right hand side of this equation has the same dimension as left hand side of the equation, hence this equation is dimensionally correct.

Discussion

93.	A physical quantitiy X is related to four measurable quantities, a,b,c and d as give `X=a^(2)b^(3)c^(5//2)d^(-2)`. The percentage error in the measurement of `a,b,c` and d are 1%,2%,2% and 4% respectively. What is the percentage error in quantitiy X?A. 0.15B. 0.17C. 0.21D. 0.23
Answer» Correct Answer - C As `X=a^(2)b^(3)c^(5//2)d^(-2)` the percentage error in X is `(DeltaX)/(X)xx100=[2((Deltaa)/(a))+3((Deltab)/(b))+(5)/(2)((Deltac)/(c))+2((Deltad)/(d))]xx100` `=2xx1%+3xx2%+(5)/(2)xx2%+2xx4%=21%`

Discussion

94.	If the fundamental units of length, mass and time are doubled, the unit of force willA. doubledB. halvedC. remain sameD. four times
Answer» Correct Answer - C `n_(1) u_(1) = n_(2) u_(2) 28` Substitute D.F of quantities

Discussion

95.	The units of length, velocity and force are doubled. Which of the following is the correct change in th other units?A. Unit of time is doubledB. Unit of mass is doubledC. Unit of momentum is doubledD. Unit of energy is doubled
Answer» Correct Answer - C

Discussion

96.	The dimensions of `K` in the equation `W=1/2Kx^(2)` isA. `[M^1L^0T^(-2)]`B. `[M^0L^1 T^(-1)]`C. `[M^1L^1T^(-2)]`D. `[M^1 L^0 T^(-1)]`
Answer» Correct Answer - 1

Discussion

97.	Given `M` is the mass suspended from a spring of force constant. `k`.The dimensional formula for `[M//k]^(1//2)` is same as that forA. frequencyB. time periodC. velocityD. wavelength
Answer» Correct Answer - B Here `[K] = "force"//"length" = ML^(0)T^(-2)` Hence `[(M)/(k)]^(1//2) = M^(0) L^(0) T`

Discussion

98.	Frequency is the function of density `(rho)` , length `(a)` and surface tension `(T)` . Then its value isA. `krho^(1//2) l^(3//2) T^(-1//2)`B. `krho^(3//2) l^(3//2) T^(-1//2)`C. `krho^(1//2) l^(3//2) T^(-3//4)`D. `kT^(1//2) rho^(-1//2) l^(-3//2)`
Answer» Correct Answer - 4

Discussion

99.	STATEMENT-1 The accuracy in final result of an experiment is always less than the accuracy of any one of the quantities used to find it STATEMENT-2 The accuracy with which you can report any reading depends on least count of measuring instrument STATEMENT-3 Making a number of readings of a given quantity and taking an average will reduce the systematic errorsA. TFTB. TTTC. FFTD. TTF
Answer» Correct Answer - 4

Discussion

100.	The length of a pendulum is measured as 20.0 cm. The time interval for 100 oscillations is measured as 90 s with a stop watch of 1 s resolution. Find the approximate percentage change in g.
Answer» Correct Answer - 3

Discussion

Explore topic-wise InterviewSolutions in .

The solid angle subtended by the periphery of an area `1cm^(2)` at a point situtated symmetrically at a distance of 5 cm from the area isA. `2xx10^(-2)` steradianB. `4xx10^(-2)` steradianC. `6xx10^(-2)` steradianD. `8xx10^(-2)` steradian

A drop of olive oil of radius 0.25 mm spreads into a circular film of radius 5 cm on the water surface. Estimate the molecular size of the olive oil

If the average life of a person is taken as 100 s the age of the universe on this scale is of the orderA. `10^(10)s`B. `10^(8)s`C. `10^(17)s`D. `10^(9)s`

10 drops of an oleic acid solution of concentration `1/400 cm^3` per `cm^3` of alcohol, are dropped on a water surface. The circular film thus produced has radius 10 cm. Find the molecular size of oleic acid, if the radius of each drop is 1.4 mm.

If a human heart beats once in every 0.8 s, find the number of times it has beaten in the life of a 10 year old boy

Which of the following physical quantities has same unit in all the three system of units?A. massB. lenthC. timeD. none of these

You measure two quantities as `A=1.0m+-0.2m`,`B=2.0m+-0.2m`. We should report correct value for `sqrt(AB)` asA. `1.4m+-0.4m`B. `1.41m+-0.15m`C. `1.4m+-0.3m`D. `1.4m+-0.2m`

You measure two quantities as `A=1.0m+-0.2m`,`B=2.0m+-0.2m`. We should report correct value for `sqrt(AB)` asA. `1.4m+-0.4m`B. `1.41m+-0.15m`C. `1.4m +-0.3 m`D. `1.4 m+-0.2m`

The following is a unitless and dimensionless quantityA. AngleB. Solid angleC. Mechanical equivalent of heatD. Coefficient of friction

A dimensionless quantity y is represented by the formula `y=(a-bc)/(d+e)`. Which of following is/arecorrect?A. Dimensions of d and e are sameB. abc and de have same dimensionsC. `"bc"/"ae+d"` is dimensionlessD. de+dc is not meaningful

Let `y=A sin (omegat-kx)` represent the variation of distance y of a particle with time t. Which of the following is not meaningful?A. `y/A+omega`B. `y/omega+"At"/"kx"`C. A-kxD. `A+omega/k`

The displacement of a progressive wave is represented by `y = A sin (omegat - kx),` where x is distance and t is time. Write the dimensional formula of (i) `omega` and (ii) k.

Time for 20 oscillations of a pendulum is measured as `t_1 = 39.6 s , t_2 = 39.9 s , t_3 = 39.5.` What is the precision in the measurements ? What is the accuracy of the measurement ?

A physical performs an experiment and taken 200 readings. He repeats the same experiment and now takes 800 readingbs. By doing soA. the probable error remains sameB. the probable error is four timesC. the probable error is halvedD. the probable error si reduced by a factor `¼`

The erros that always occur in the measurement with screw gauge isA. random errorsB. systematic errorsC. gross errorsD. neglibible errors

If in a Vernier callipers 10 VSD coincides with 8 MSD, then the least count of Vernier calliper is [given 1 MSD = 1mm]A. `1xx10^(-4)m`B. `2xx10^(-4)m`C. `1xx10^(-3)m`D. `8xx10^(-4)m`

Dimension of resistance in an elecatrical circuit, in terms of dimension of mass `M`, of length `L`, of time `T`, and of current `I`, would beA. `[ML^(2)T^(-3)I^(-2)]`B. `[ML^(2)T^(-3)I^(-1)]`C. `[ML^(2)T^(-2)]`D. `[ML^(2)T^(-1)I^(-1)]`

In Column-I, some physical quantities are given and in column-II, dimensions of the physical quantities are given . Match the entries in column-I to each entry in Column-II.

match the following

If the unit of force is 1 kN, unit of length 1 km and unit of time is 100s, what will be the unit of mass?A. 1000 kgB. 1 kgC. 10000 kgD. 100 kg

The dimension of magnetic field in `M,L,T and C` (coulomb) is given as

The respective number of signficant figures for the numbers `23.023, 0.0003 and 2.1 xx 10^(-3)` are

A stick has a length of `12.132cm` and an other stick has a length of `12.4cm` then the total length of the stick is...........A. `24.53cm`B. `24.5 cm`C. `2.overline(45) cm`D. `2.453cm`

The number of significiant figures in `5.69 xx 10^(15) kg` isA. `1`B. `2`C. `3`D. `4`

How many light years alpha centauri away from the earth?A. 1.29B. 2.29C. 3.29D. 4.29

Which of the following pairs of physical quantities have same dimensions?A. Force and powerB. Torque and energyC. Torque and powerD. Force ad torque.

A dimensionless quantityA. never has a unitB. always has unitC. may have a unitD. does not exit

Light year is a unit ofA. DistanceB. timeC. speedD. intensity of light

Which one of the following methods is used to measure distance of a planet or a star from the earth?A. Echo methodB. Parallax methodC. Triangulation methodD. none of these

In the relation P=`alpha/beta , e^((alphax)/(nR theta))` , P is power , x is distance n is number of moles, R is gas constant and `theta` is temperature dimensional formula of `beta` isA. `[M^0L^0T^0]`B. `[M^(-1)L^0T^1]`C. `[M^0L^(-1)T^1]`D. `[M^0L^(-1)T^(-1)]`

A student performs exeriment with simple pendulum and measures time for `10` vibrations. If the measures the time for `100` vibrations, the error in measurement of time period will be reduced by a factor of......A. `10`B. `90`C. `100`D. `1 overline(0)00`

The frequency `f` of vibrations of a mass `m` suspended from a spring of spring constant `k` is given by `f = Cm^(x) k^(y)` , where `C` is a dimensionnless constant. The values of `x and y` are, respectively,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`

The frequency `f` of vibrations of a mass `m` suspended from a spring of spring constant `k` is given by `f = Cm^(x) k^(y)` , where `C` is a dimensionnless constant. The values of `x and y` are, respectively,A. `(1)/(2),(1)/(2)`B. `-(1)/(2),-(1)/(2)`C. `(1)/(2),-(1)/(2)`D. `-(1)/(2),(1)/(2)`

If `L, R , C , and V`, respectively , represent inductance , resistance , capacitance and potential difference , then the dimensions of `L //RCV` are the same as those ofA. ChargeB. `1//"Charge"`C. CurrentD. `1//"Current"`

The length of a rod is measured as `35.3cm` then the gradutions ont eh scale are up toA. `1cm`B. `1mm`C. `0.01mm`D. `0.1mm`

A physical quantitiy X is related to four measurable quantities, a,b,c and d as give `X=a^(2)b^(3)c^(5//2)d^(-2)`. The percentage error in the measurement of `a,b,c` and d are 1%,2%,2% and 4% respectively. What is the percentage error in quantitiy X?A. 0.15B. 0.17C. 0.21D. 0.23

If the fundamental units of length, mass and time are doubled, the unit of force willA. doubledB. halvedC. remain sameD. four times

The units of length, velocity and force are doubled. Which of the following is the correct change in th other units?A. Unit of time is doubledB. Unit of mass is doubledC. Unit of momentum is doubledD. Unit of energy is doubled

The dimensions of `K` in the equation `W=1/2Kx^(2)` isA. `[M^1L^0T^(-2)]`B. `[M^0L^1 T^(-1)]`C. `[M^1L^1T^(-2)]`D. `[M^1 L^0 T^(-1)]`

Given `M` is the mass suspended from a spring of force constant. `k`.The dimensional formula for `[M//k]^(1//2)` is same as that forA. frequencyB. time periodC. velocityD. wavelength

Frequency is the function of density `(rho)` , length `(a)` and surface tension `(T)` . Then its value isA. `krho^(1//2) l^(3//2) T^(-1//2)`B. `krho^(3//2) l^(3//2) T^(-1//2)`C. `krho^(1//2) l^(3//2) T^(-3//4)`D. `kT^(1//2) rho^(-1//2) l^(-3//2)`

The length of a pendulum is measured as 20.0 cm. The time interval for 100 oscillations is measured as 90 s with a stop watch of 1 s resolution. Find the approximate percentage change in g.