InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The dinesity of meterial in CGS system of mass is `4g cm^(3)` in a system of unit in which unit of length is `10 cm` and unit of mass is `100g` the value of density of meterial will beA. 400B. 0.04C. 0.4D. 40 |
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Answer» Correct Answer - D (4) Dimensions of density : `ML^(-3)` `n_(1) u_(1) = n_(2) u_(2)` `n_(2) = n_(1) (u_(1))/(u_(2)) = n_(1) [(M_(1))/(M_(2))] [(L_(1))/(L_(2))]^(-3)` Here, `n_(1) = 4, M_(1) = 1 g, L_(1) = 1 cm` `M_(2) = 100 g, L_(2) = 10 cm` `n_(2) = 4 [(1)/(100 g)] [(1cm)/(10 cm)]^(-3)` `= 4 ((1)/(100)) (10)^(3) = 40` |
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| 2. |
(a) The unit of coefficient of viscosity in `CGS` system is poise `(g//cm .s)` Convert it into `SI` unit. (b) The SI unit of work is joule, convert it into `CGS` unit. |
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Answer» The dimension of coeficient of viscosity is `[ML^(-1) T^(-1)]` 1 poise `= 1 g//m.s` `SI` unit `= 1 kg//m.s` `(SI u ni t)/(1 poise) = ((1 kg)/(1 g)) ((1 m)/(1 cm))^(-1) ((1s)/(1s))^(-1)` `= ((1000)/(1 g)) ((100 cm)/(1 cm))^(-1) ((1s)/(1s))^(-1)` `= 1000 xx ((1)/(100)) = 10` `1 poise = (1)/(10) SI unit` `= (1)/(10) kg//m.s` (b) Dimensionally, energy : `[ ML^(2) T^(2)]` `(1 j o u l e)/(1 erg) = ((1 kg)/(1g)) ((1 m)/(1 cm))^(2) ((1s)/(1s))^(-2)` `= ((1000 g)/(1 g)) ((100 cm)/(1 cm))^(2)` `= 1000 xx (100)^(2) = 10^(7)` `1 j o u l e = 10^(7) erg` |
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| 3. |
A physical quantity A is related to four observable a,b,c and d as follows, `A=(a^2b^3)/(csqrtd)`, the percentage errors of measurement is a,b,c and d,are `1%`,`3%`,`2%` and `2%` respectively. What is the percentage error in the quantity A?A. 0.12B. 0.07C. 0.05D. 0.14 |
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Answer» Correct Answer - D |
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| 4. |
Dimensions of the following three quantities are the sameA. Work, energy, forceB. Velocity, momentum, impulseC. Potential energy, kinetic energy, momentumD. Pressure, stress, coefficient of elasticity |
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Answer» Correct Answer - D |
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| 5. |
The quantities `A and B` are related by the relation `A//B = m`, where `m` is the linear mass density and `A` is the force , the dimensions of `B` will beA. PressureB. WorkC. Latent heatD. None of the above |
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Answer» Correct Answer - C |
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| 6. |
Dimension of `CR` are those ofA. FrequencyB. EnergyC. Time periodD. Current |
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Answer» Correct Answer - C |
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| 7. |
The physical quantity that has no dimensions is:A. Angular VelocityB. Linear momentumC. Angular momentumD. Strain |
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Answer» Correct Answer - D |
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| 8. |
The dimensions of couple are _______A. `ML^(2)T^(-2)`B. `MLT^(-2)`C. `ML^(-1)T^(-3)`D. `ML^(-2)T^(-2)` |
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Answer» Correct Answer - A |
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| 9. |
Dimensions of magnetic field intensity isA. `[M^(0)L^(-1)T^(0)A^(1)]`B. `[MLT^(-1)A^(-1)]`C. `[ML^(0)T^(-2)A^(-1)]`D. `[MLT^(-2)A]` |
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Answer» Correct Answer - C |
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| 10. |
The speed `v` of a satellite moving in a circular orbit around the earth depends on the gravitational constant `G`, mass of the earth `m_(e)` and radius of circular orbit `r`. Estabish the relation using dimensions. |
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Answer» `v = fn (G, m_(e), r)` `v prop G^(a) M_(c )^(b) r^(c )` `[LT^(-1)] prop [M^(-1) L^(3) T^(-2)]^(a) [M]^(b) [L]^(c )` `M^(0) L^(1) T^(-1) prop M^(-a + b) L^(3a + c) T^(-2a)` Comparing powers of `M, L` and `T` `-a + b = 0` `3a + c = 1` `- 2a = - 1` `a = (1)/(2), b = - (1)/(2), c = - (1)/(2)` `v prop G^((1)/(2)) M_(e)^((1)/(2)) r^(-(1)/(2)) implies v prop sqrt((G M_(e))/(r)) implies v = k sqrt((G M_(e))/(r))` From experiment, `k = 1` `v = sqrt((G M_(e))/(r))` |
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| 11. |
The buoyant force `F` acting on a body depends on the density of medium `rho`, volume of body immerese `V` and acceleration due to gravity `g`. Establish the relation using method of dimensions. |
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Answer» `F = fn (rho, V, g)` `F prop rho^(a) V^(b) g^(c )` `[MLT^(-2)] prop [ML^(-3)]^(a) [L^(3)]^(b) [LT^(-2)]^(c )` `M^(1) L^(1) T^(-2) prop M^(a) L ^(-3a + 3b + c) T^(-2c)` Comparing power of `M, L` and `T`, `a = 1` `- 3 a + 3 b+ c = 1` `- 2c = - 2` `a = 1, b = 1, c = 1` `F prop rho v g implies F = k rho Vg` From experiments, `k = 1` `F = rho Vg` |
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| 12. |
The velocity of water wave `v` may depend on their wavelength `lambda`, the density of water `rho` and the acceleration due to gravity `g`. The method of dimensions gives the relation between these quantities asA. `v^(2) prop lambda g rho`B. `v^(2) prop lambda^(-1) g^(-1) rho^(-1)`C. `v^(2) prop g lambda`D. `v^(2) prop rho lambda` |
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Answer» Correct Answer - C (3) `v prop lambda^(a) rho^(b) g^(c )` `LT^(-1) prop [L]^(a) [ML^(-3)]^(b) [LT^(-2)]^(c )` `M^(0) L^(1) T^(-1) prop M^(b) L^(a - 3b + c) T^(-2c)` Comparing powers of `M, L` and `T` `b = 0` `a - 3b + c = 1` `- 2c = - 1 implies c = (1)/(2)` `v prop lambda^(1//2) g^(1//2)` `v^(2) prop lambda g` |
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| 13. |
The dimensional formula for angular momentum isA. `ML^(2)T^(-2)`B. `ML^(2)T^(-1)`C. `MLT^(-1)`D. `M^(0)L^(2)T^(-2)` |
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Answer» Correct Answer - B |
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| 14. |
If velocity v acceleration A and force F are chosen as fundamental quantities, then the dimensional formula of angular momentum is terms of v,A and F would beA. `FA^(-1)v`B. `Fv^(3)A^(-2)`C. `Fv^(2)A^(-1)`D. `F^(2)v^(2)A^(-1)` |
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Answer» Correct Answer - B |
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| 15. |
The values of two resistors are `(5.2pm0.2)" k"Omega` and `(10.0pm0.1)" k"Omega`. What is the percentage error in the equivalent resistance when they are connected in parallel?A. 0.02B. 0.05C. 0.07D. 0.1 |
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Answer» Correct Answer - B |
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| 16. |
By what percentage should the pressure of a given mass of a gas be increased so as to decrease its volume by 10% at a constant temperature?A. 0.05B. `7.2`%C. `12.5`%D. `11.1`% |
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Answer» Correct Answer - D When `T` is constant, `pV` = constant. When volume is decreased by 10% that is volume becomes `(90)/(100)`, the pressure must become `100//90`. Thus, percentage increase in pressure `=((100-90)xx100)/(90)=11.1%` |
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| 17. |
If voltage `V=(100pm5)` V and current `I=(10pm0.2)` A, the percentage error in resistance `R` isA. `5.2`%B. 0.25C. 0.07D. 0.1 |
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Answer» Correct Answer - C Given, voltage, `V=(100pm5)`V Current, `I=(10pm0.2)`A `therefore` Resistance, `R=(V)/(I)` Maximum percentage error in resistance `((DeltaR)/(R)xx100)=((DeltaV)/(V)xx100)+((DeltaI)/(I)xx100)` =`((5)/(100)xx100)+((0.2)/(10)xx100)` = 5+2=7% |
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| 18. |
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` |
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Answer» Correct Answer - D |
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| 19. |
Which pair has the same dimensionsA. Work and powerB. Density and relative densityC. Momentum and impulseD. Stress and strain |
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Answer» Correct Answer - C |
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| 20. |
Select the pair whose dimensions are sameA. Pressure and stressB. Stress and strainC. Pressure and forceD. Power and force |
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Answer» Correct Answer - A |
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| 21. |
if the randon error in the arithmetic mean of 50 observations is `alpha`, then the random error in the arithmetic mean of 150 observations would beA. `alpha`B. `3alpha`C. `(alpha)/(3)`D. `2alpha` |
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Answer» Correct Answer - C |
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| 22. |
Assersion : Out of three meansurements `l = 0.7 m, l = 0.70m` and `l = 0.700m` the last one is most accurate. Reason: In every meansurements only the last significant digit is not accurately known.A. If both assertion and reason are true and the reason is the correctexplanation of the assertion.B. If both assertion and reason are true but reason is not the correctexplanation of the assertion.C. If assertion is true but reason is false.D. If the assertion and reason both are false. |
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Answer» Correct Answer - B |
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| 23. |
With the usual notations the following equation `S_(t)=u+1/2a(2t-1)` isA. Only numerically correctB. Only dimensionally correctC. Both numerically and dimensionally correctD. Neither numerically nor dimensionally correct |
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Answer» Correct Answer - C |
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| 24. |
Find the dimension of the quantity L/(RCV), where symbols have usual meaning.A. `[A]`B. `[A^(2)]`C. `[A^(-1)]`D. None of these |
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Answer» Correct Answer - C |
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| 25. |
Which is not a unit of electric fieldA. `NC^(-1)`B. `Vm^(-1)`C. `JC^(-1)`D. `JC^(-1)m^(-1)` |
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Answer» Correct Answer - C |
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| 26. |
The correct value of `0^(@)C` on the Kelvin scale isA. `273.15K`B. `272.85K`C. `273K`D. `273.2K` |
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Answer» Correct Answer - A |
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| 27. |
`Joulexxsecond` is the unit ofA. EnergyB. momentumC. angular momentumD. power |
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Answer» Correct Answer - C Since `(mvr)=n.(h)/(2pi)` and `E=hv` So, unit of `h` = joule second = angular momentum |
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| 28. |
The time period of a simple pendulum is given by `T = 2 pi sqrt(L//g)`, where `L` is length and `g` acceleration due to gravity. Measured value of length is `10 cm` known to `1 mm` accuracy and time for 50 oscillations of the pendulum is 80 s using a wrist watch of 1 s resloution. What is the accuracy in the determination of `g`? |
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Answer» `T = 2 pi sqrt((L)/(g))` `g = (4 pi^(2) L)/(T^(2))` Here `T = (t)/(n), t:` total time, `n` : number of oscillaiton `Delta T = (Delta t)/(n)` `(Delta T)/(T) = (Delta t)/(t)` Maximum relative errors in `g` `(Delta g)/(g) = (Delta L)/(L) + 2 (Delta T)/(T)` Maximum percentage error is `g` `(Delta g)/(g) xx 100 = (Delta L)/(L) xx 100 + 2 (Delta T)/(T) xx 100` `= (0.1)/(10) xx 100 + 2 (1)/(80) xx 100` `= 1 + 2.3 = 3.5%` |
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| 29. |
If momentum, time and energy were chosen as basic quantities, find dimensions of (a) mass and (b) force. |
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Answer» The dimension for momentum, time and energy are `p = [MLT^(-1)]` `t = [T]` `E = [ML^(2) T^(-2)]` (a) `m prop p^(a) t^(b) E^(c )` `M prop [MLT^(-1)]^(a) [T]^(b) [ML^(2) T^(-2)]^(c )` `M^(1) L^(0) T^(0) prop M^(a + c) L^(a + 2c) T^(-a + b - 2c)` Comparing power of `M, L` and `T` `a + c = 1` `a + 2c = 0` `-a + b - 2c = 0` Solving we get `C = - 1, a = 2, b = 0` `m prop p^(2) E^(-1)` (b) `F prop p^(a) t^(b) E^(c )` `MLT^(-2) prop [MLT^(-1)]^(a) [T]^(b) [ML^(2) T^(-2)]^(c)` `M^(1) L^(1) T^(-2) prop M^(a + c) L^(a + 2c) T^(- a + b + 2c)` Comparing power of `M, L` and `T` `a + c = 1` `a + 2c = 1` `-a + b - 2c = -2` `c = 0, a = 1, b = - 1` `F prop p t^(-1)` |
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| 30. |
The temperatures of two bodies measured are `theta_(1) = 10^(@)C +- 0.4^(@)C` and `theta_(2) = 10^(@)C +- 0.3^(@)C`. Find the sum and difference in temperatures with error limits. |
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Answer» `theta_(1) = (10 +- 0.4)^(@)C` `theta_(2) = (40 +- 0.3)^(@)C` `Delta theta = +- (Delta theta_(1) + Delta theta_(2))` `= +- (0.4 + 0.3)^(@)C` `= +- 0.7^(@)C` `theta_(1) + theta_(2) = 10 + 40 = 50^(@)C` `theta_(2) - theta_(1) = 40 - 10 = 30^(@)C` Hence sum of temperature `= (50 +- 0.7 )^(@)C` Difference of temperatures `= (30 +- 0.7)^(@)C` |
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| 31. |
Assertion : `L//R and CR` both have same dimensions Reason `L//R and CR` both have dimensions of timeA. If both Assertion and Reason are correct and Reason is the correct explaination of Assertion.B. If both Assertion and Reason are correct but Reason is not the correct explaination of Assertion.C. If Assertion is true but Reason is false.D. If Assertion is false but Reason is true. |
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Answer» Correct Answer - A `L//Rand CR` both have dimensions of time. |
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| 32. |
If c and R denote capacity and resistance the dimensions of CR are :A. `[M^(0)L^(0)T]`B. `[ML^(0)T]`C. `[M^(0)L^(0)T^(2)]`D. not expressible in terms of M,L and T |
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Answer» Correct Answer - A `CR` is time constant. |
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| 33. |
Errror in the measurement of radius of a sphere is `1%` .The error in the calculated value of its volume isA. 0.01B. 0.03C. 0.05D. 0.07 |
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Answer» Correct Answer - B |
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| 34. |
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)]` |
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Answer» Correct Answer - B |
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| 35. |
Assertion : A screw gauge having a smaller value of pitch has greater accuracy. Reason : The least count of screw gauge is directly proportional to the number of divisions on circular scale.A. If both Assertion and Reason are correct and Reason is the correct explaination of Assertion.B. If both Assertion and Reason are correct but Reason is not the correct explaination of Assertion.C. If Assertion is true but Reason is false.D. If Assertion is false but Reason is true. |
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Answer» Correct Answer - C |
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| 36. |
The length of a uniform rod is 100.0 cm. If length is measured with a meter rod having least count 1 mm and radius is measured with vernier callipers having least count 0.1 mm, the percentage error in calculated volume of cylinder isA. 0.021B. 0.03C. 0.0201D. 0.032 |
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Answer» Correct Answer - A |
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| 37. |
`{:(,"Column I",,"Column II"),(("A"),"Electrical resistance",(p),["M"^(-1)"L"^(-2)"T"^(4)"A"^(2)]),(("B"),"Capacitance",(q),["ML"^(2)"T"^(-2)"A"^(-2)]),(("C"),"Magnetic field",(r),["ML"^(2)"T"^(-3)"A"^(-2)]),(("D"),"Inductance",(s),["MT"^(-2)"A"^(-1)]):}` |
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Answer» Correct Answer - `("A"to"r","B"to"p","C"to"s","D"to"q")` |
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| 38. |
The equation of state of some gases can be expressed as `(P + (a)/(V^(2))) = (R theta)/(V)` where P is the pressure V the volume,` theta`The temperature and a and b are constant .The dimensional formula of a isA. `["ML"^(5)"T"^(2)]`B. `["ML"^(-1)"T"^(-2)]`C. `["L"^(3)]`D. `["L"^(6)]` |
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Answer» Correct Answer - A |
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| 39. |
A physical quantity `x` depends on quantities `y and z` as follows : ` x = Ay + B tan ( C z)`, where `A , B and C` are constants. Which of the followings do not have the same dimensions?A. `x` and `b`B. `C` and `z^(-1)`C. `y` and `B//A`D. `x` and `A` |
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Answer» Correct Answer - D |
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| 40. |
Which one of the following pairs of quantities and their units is aproper matchA. Electric field -Coulomb/mB. Magnetic flux-WeberC. Power-FaradD. Capacitance -Henry |
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Answer» Correct Answer - B |
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| 41. |
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)` |
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Answer» Correct Answer - B (2) `h = (1)/(2) g t^(2) implies g = (2h)/(t^(2))` `(Delta g)/(g) = (Delta h)/(h) + 2 (Delta t)/(2)` `(Delta g)/(g) xx 100 = (Delta h)/(h) xx 100 + 2 (Delta t)/(t) xx 100` `= e_(1) + 2 e_(2)` |
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| 42. |
Which of the following measurement is most precise?A. 5.00 mmB. 5.00 cmC. 5.00 mD. 5.00 km |
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Answer» Correct Answer - A All given measurements are correct upto two decimal places. As here 5.00 mm has the smallest unit and the error in 5.00 mm is least (commonly taken as 0.01 mm if not specified), hence, 5.00 mm is most precise. Note : In solving these type of quentions, we should be careful about units although their magnitude is same. |
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| 43. |
The mean length of an object is `5cm`. Which of the following measurement is most accurate?A. 4.9 cmB. 4.805 cmC. 5.25 cmD. 5.4 cm |
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Answer» Correct Answer - A Given length, `l` = 5 cm Now, checking the errors with each options one by one, we get `Deltal_(1)`=5-4.9=0.1 cm `Deltal_(2)` = 5-4.805=0.195 cm `Deltal_(3)` = 5.25-5=0.25 cm `Deltal_(4)` = 5.4-5=0.4 cm Error `Deltal_(1)` is least. Hence, 4.9 cm is most accurate. |
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| 44. |
One second is equal toA. 1650763-73 time periods of Kr clockB. 652189.63 time periods of Kr clockC. 1650763.73 time periods of Cs clockD. 9192631770 time periods of Cs block |
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Answer» Correct Answer - D |
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| 45. |
The resistance `R = V//i`, where `V = 100 +- 5 V and I = 10+- 0.2 A`. What is the total error in `R`?A. `5%`B. `7%`C. `5.2%`D. `5/2%` |
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Answer» Correct Answer - B |
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| 46. |
The unit of Young’s modulus isA. `Nm^(2)`B. `Nm^(-2)`C. `Nm`D. `Nm^(-1)` |
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Answer» Correct Answer - B |
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| 47. |
`1kWh=`A. `1000W`B. `36xx10^(5)J`C. `1000J`D. `3600J` |
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Answer» Correct Answer - B |
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| 48. |
A cube has numerically equal volume and surface area. The volumeof such a cube isA. 216 unitsB. 1000 unitsC. 2000 unitsD. 3000 units |
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Answer» Correct Answer - A |
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| 49. |
The units of angular momentum areA. `kg-m^(2)//s^(2)`B. Joule-sC. Joule/sD. `kg-m-s^(2)` |
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Answer» Correct Answer - B |
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| 50. |
What is the number of significant figure in (3.20 + 4.80) `""xx10^(5)`?A. 5B. 4C. 3D. 2 |
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Answer» Correct Answer - C |
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