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. |
A gas bubble , from an explosing under water , oscillates with a period T proportional in `P^(0)D^(0)E^(0)` , where p is the static prossure , d is the density of water and E is the total energy of the explosion . Find the value of` a , b` and` c` . |
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Answer» Correct Answer - A::B::C `[T] = [p^(a)d^(b) E^(c)] = [ML^(-1)T^(-2)] ^(0) [ML^(-3)]^(4)[ML^(2)T^(-2)]^(1)` Equating the power of both sides , we have ` a+ b+ c= 0 ` …(i) ` -a - 3b + 2c = 0` …(ii) ` -2a - 2c =1 ` …(iii) Solving these three equation , we have ` a = (5)/(6) , b = (1)/(2)` and ` c = (1)/(3) ` |
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| 2. |
In a view unit system, 1 unit of time is equal to 10 second, 1 unit of mass is `5 kg` and 1 unit of length is `20 m`. In the new system of units 1 unit of energy is equal to :A. 20 jouleB. `(1)/(20)` jouleC. 4 jouleD. 16 joule |
| Answer» Correct Answer - A | |
| 3. |
The dimensins of `a/b` in the equation `P=(a-t^(2))/(bx)` where `P` is pressure `x` is distance and `t` is time, areA. `[M^(2)LT^(-3)]`B. `[MT^(-2)]`C. `[LT^(-3)]`D. `[ML^(3)T^(-1)]` |
| Answer» Correct Answer - B | |
| 4. |
A cube has a side of length `1.2 xx 10^(-2)m`. Calculate its volume.A. `1.7 xx 10^(-6)m^(3)`B. `1.73 xx 10^(-6) m^(3)`C. `1.70 xx 10^(-6) m^(3)`D. `1.732 xx 10^(-6)m^(3)` |
| Answer» Correct Answer - A | |
| 5. |
`A` quantity` X` is given by `epsilon_(p) L(delta V)/(delta t)` , where `epsilon_(p)` is the permitivity of free space ,L is a length , `delta V` is a potential diffrence and ` deltat ` is a time interval . The dimensional formula for `X` is the seme as that ofA. resistanceB. chargeC. voltageD. current |
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Answer» Correct Answer - D `C = (Delta q)/(Delta V) = (epsilon_(0)A)/(d)` or ` epsilon_(0) = (A)/(L) = (Delta q)/(DeltaV) ` or ` epsilon_(0) = ((Delta q) L)/(A(Delta V))` ` X = epsilon_(0) L (Delta V)/(Delta t)` ` = ((Delta q)L)/(A(DeltaV)) L (Delta V)/(Delta t) ` but ` [A] = [L^(2)]` :.` X = (Delta q)/(Delta t) = current` |
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| 6. |
Given that` y = A sin [((2 pi )/(lambda)(ct - x))]` where` y` and `x` are measured in metres ,Which of the following statements is true ?A. The unit of ` lambda`is same as that of` x `and` A`B. The unit of `lambda ` is same as that of `x` but not of ` A`C. The unit of c is same as that of `(2 pi)/(lambda)`D. The unit of `(a -x )` is same as that of `(2 pi)/(lambda)` |
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Answer» Correct Answer - A ` :.(2 pi r)/(lambda)` is dimensionless `:. [lambda] = [x] = [L] = [A]` |
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| 7. |
The equation of a wave is given by `y = a sin omega [(x)/v -k]` where ` omega ` is angular velocity and v is the linear velocity . The dimensions of k will beA. `[T^(2)]`B. `[T^(-1)]`C. `[T]`D. `[LT]` |
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Answer» Correct Answer - C `omega k` is dimensionless ` [k] = [(1)/(omega)] = [T]` |
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| 8. |
The contripetal force F acting on a particle moving uniformly in a circle may depend upon mass (m), velocity (v) and redio ( r) of the circle . Derive the formula for F using the method of dimensions. |
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Answer» Let `F = k(m)^(x) (v)^(y) ( r)^(z)` ..(i) Here ,k is a dimensionless constant of proportionality . Writing the dimensions of RHS and LHS in EQ , (i) , we have ` [MLT^(-2)] = [M]^(x)[LT^(-1)]^(y) [L]^(z) = [M^(z) L^(y+z)T^(-y)] ` Equating the power of M,L and T of both side , we have , `x= 1, y= 2, and y+z= 1 or z= 1-y = -1` Puting the value in Eq , (i) we gwt `F = kmv^(2)(r^(-1)) = k(mv^(2))/(r)` or `F= (mv^(2))/(r)` (where`k=1`) |
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| 9. |
Write the dimensions of a and b in the relation ,` P = (b-x^(2))/(at)` , where P is power ,x is distance and t is time |
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Answer» The given equation can be written as, `Pat = b-x^(2)` Now, ` [Pat] = [b] =[ x^(2)]` or`[b]=[ x^(2)] = [M^(0)L^(2)T^(0)]` and ` [a] = ([x^(2)])/([Pt]) ([L^(2)])/([ML^(2)T^(-3)][T]) = [M^(-1)L^(0)T^(0)]` |
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| 10. |
If unit of length and time is doubled the numerical value of g (acceleration due to gravity ) will beA. doubledB. halvedC. four timeD. same |
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Answer» Correct Answer - B If unit of length and time is double , then value of g will be halved |
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| 11. |
In the formula , `p = (nRT)/(V-b) e ^(a)/(RTV)` find the dimensions of a and b, where p = pressure , n= number of moles , T = temperture , V = volume and E = universal gas constant . |
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Answer» Correct Answer - A::B::C `[(a)/(RTV)]=[M^(0)L^(0)T^(0)]` `rArr [a]=[RTV]` `][ML^(2)T^(-2)][L^(3)]` `=[ML^(5)T^(-2)]` `[b]=[V]=[L^(3)]` |
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| 12. |
Write the dimensions of the following in the terms of `"mass" , "time" , "length and charge"` (a) Megnetic flux (b) Rigulity modus. |
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Answer» Correct Answer - A::B (a) magnetic flux , `phi = Bs = ([F])/([q^(v)])(s)` ` :. [phi] = [(Fs)/(q^(v))] = [[MLT^(-2)L^(-2))/(QLT^(-1))]` ` = [ML^(2)T^(-1)Q^(-1)]` (b) [kindly Modulus] = `([F)/(A)] = ([MLT^(-1))/(L^(2))]` `=[ML^(-1)T^(-2)]` |
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| 13. |
In the relaction ` p = (a)/(beta) e ^((aZ)/(k theta )`, p is pressure Z is distance .k is Boltamann constant and `theta` is the teperations . The dimensional formula of `beta` will beA. `[M^(0)L^(2)T^(0)]`B. `[ML^(2)T]`C. `[ML^(0)T^(-1)]`D. `[M^(0)L^(2)T^(-1)]` |
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Answer» Correct Answer - A `[(aZ)/(ktheta)] = [M^(0) L^(0) T^(0) ]` `[a] = [(k theta )/(Z)]` `[p] = [(a )/(beta)]` `[beta] = [(a )/(p)] = [(k theta )/(Zp)]` Demension of k theta are that to energy ,.Hence , ` [beta] = [(ML^(2)T^(-2))/(LML^(-1)T^(-2))] ` ` = [M^(0)L^(2)T^(0)]` |
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| 14. |
The `SI` unit of inductance, the henry can be written asA. weber/ampersB. volt -second /ampereC. `"joule" //("ampere")^(2)`D. ohm - second |
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Answer» Correct Answer - A::B::C::D (a) `L = (phi )/(i) or henry = ("weber")/("ampere")` (b) ` e = - L ((dl)/(dt)) rArr :. L= -e/((dl//dt))` or `"henry" = ("volt - second")/("ampare")` (c) ` U = (1)/(2) Li^(2) rArr :. L = (2U)/(t^(2)) ` or henry =` ("joule")/(("ampere")^(2)) ` (d) ` U = (1)/(2) Li^(2) = i^(2) Rt ` :. ` L = Rt or benry = ohm - second ` |
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| 15. |
Taking `"force" F, "length" L and "time" T` to be the fundemental equations , find the dimensions of (a) density (b) pressure (c ) momentun and (d) energy |
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Answer» Correct Answer - A::B::C::D (a) `["density"] = [F]^(x)[L]^(y) [T]^(z)` ` :. [ML^(-3)] = [MLT^(-2)]^(x)[L]^(y)[T]^(z)` Equation the powers we get , `x = 1, y = -4` and `z= 2` :. `["density"] ` = [FL^(-4)T^(2)]` in the similar maner , other parts can be solved. |
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| 16. |
L,C and R represent the physical quantities inductance, capacitance and resistance respectively. Which of the following combinations have dimensions of frequency?A. `(t)/(RC)`B. ` (R )/(L)`C. `(1)/(sqrt(LC)`D. `( c )/(L)` |
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Answer» Correct Answer - A::B::C `Cp` and `(L)/(R )` both are time constent . Their unit is second ` (1)/(CR) ` and` ( R )/(L)` have the SI unit `("second") ^(-1)` Farther . Resonance frequency omega ` = (1)/(sqrt LC) ` |
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| 17. |
Assertion Velocity , volume and acceleration can be taken as fundemental quantities because Reason: All the three are independent from each other .A. If both Assertion and Reson are true and the Resion is correct explanation of the AssertionB. If both Assertion and Reason are true but the correct explenation ofAssertion.C. If Assertion is true , but the Reason is false .D. If both Assertion and Reason are wrong. |
| Answer» Correct Answer - D | |
| 18. |
In the formula `X = 3Y Z^(2)` , `X` and `Z` have dimensions of capacitance and magteic induction respectively . When are the dimensions of F in MESQ system ?A. `[M^(-3)L^(-1)T^(3)Q^(4]]`B. `[M^(-3)L^(-2)T^(4)Q^(4)]`C. `[M^(-3)L^(-2)T^(4)Q^(4)]`D. `[M^(-3)L^(-2)T^(4)Q^(4)]` |
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Answer» Correct Answer - B ` [Y] =[( X)/(Z)^(2)] = [["capacitance")/(("magnetic induction")^(2))]` ` = [(M^(-1) L^(-2)Q^(2)T^(2))/(M^(2)Q^(-2)T^(-2))]` ` = [M^(-3)L^(-2)T^(4)Q^(4)] ` |
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| 19. |
Find the dimensional formula of (a) coefficient of viscosity `eta` (b)charge `q` (c ) potention `V` (d) capacitance `C` and ( e) resistance `R` Some of the equations containing these quantities are `F= -etaA [[Deltau )/(Delta ]], q = It. U = VIt, q = CV and V = IR ` where A denotes the v the velocity , I is the length ,I the electric current, t the time and U the energy . |
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Answer» (a)` eta = -(F)/(a) (Delta l)/(Delta u) rArr :.[eta] = ([F][I])/([A][v]) = ([MLT^(-2)][L])/([L^(2)][LT^(-1)]) = [ML^(-1) T^(-1)]` (b)` q= it rArr :. [q]= [I][t] = ,AT]` (c ) `U= Vit` `V = (U)/(it) or [V] = ([U])/([I][t]) = ([MLT^(-2)T^(-2)])/([A][T]) = [MLT^(2)T^(-1)]` (d) `q= CV` ` :. C= (q)/(v) ` or `[C] = ([q])/([v]) = ([AT])/([MLT^(2)T^(-3) A^(-1)]) = [M^(-1)L^(-3) T^(4)A^(2)]` (e) ` V = IR` `:. R= (V)/(T) or [R ] = ([V])/([I]) = ([ML^(2)T^(-3)A^(-1)])/([A])=[ML^(3)T^(-3)A^(-2)]` |
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| 20. |
For a moles of gas ,Van der Weals equation is `(p = (a)/(V^(-2))) (V - b) = nRT`ltbr. Find the dimensions of a `a and b `, where `p = pressure` of gas` ,V = volume` of gas and` T = temperature of gas` . |
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Answer» Correct Answer - A::B `[b] = [V] = [L^(2)]` ` ([a])/([V]^(2)) = [p] = [ML^(-1) T^(-2)]` `rArr [aa] = [ML^(2)T^(-2)]` |
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| 21. |
Chooce the wrong statement.A. All quantities may be represented dimensionally in terms of the base quantitiesB. A base quantity cannot be represented in terms of the rest of the base quantityC. The dimension of a base quantity in other base quantities is always zeroD. The dimension of a derived quantities is never seen in any base quantity |
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Answer» Correct Answer - D `phi= Bs = (F)/(IL) s = [(MLT^(-2)L^(2))/(AL)]` `[g] = LT^(-2)` |
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| 22. |
If velocity , time and force were chosen as basic quantities , find the dimensions of mass and energy . |
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Answer» we know that `"Force" ="mass" xx "acceleration"` `="mass" xx("velocity")/("time")` `"mass" =("force"xx "time")/("velocity")` `["mass"]=(["force"xx "time"])/(["velocity"])` `=([F][T])/([v])` `["mass"]=[FTv^(-1)]` Dimensions of energy are same an the dimensions of kinetic energy `["Energy" ]=[(1)/(2)mv^(2)]=[m][v]^(2)` `=[FTv^(-1)][v]^(2)` `=[FTv]` |
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| 23. |
Assertion if two physical quantities have same dimension, then they can be certainly added or subtracted because Reason if the dimension of both the quantities are same then both the physical quantities should be similar .A. If both Assertion and Reson are true and the Resion is correct explanation of the AssertionB. If both Assertion and Reason are true but the correct explenation ofAssertion.C. If Assertion is true , but the Reason is false .D. If both Assertion and Reason are wrong. |
| Answer» Correct Answer - A | |
| 24. |
Using `mass (M), "length"(L) , time (T)` and current` (A) `as fundamental quantites the demension of permeability isA. `[M^(-1)LT^(-2)A]`B. `[ML^(-2)T^(-2)A^(-1)]`C. `[MLT^(-2)A^(-2)]`D. `[MLT^(-1)A^(-1)]` |
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Answer» Correct Answer - C ` B = (mu_(0))/(2 pi) (i)/(r) ` but ` B = (F)/(il) (F= ilB)`:. `(F)/(il) = (mu_(0))/(2 pi ) (i)/(r) ` ` [mu_(0)] = [(F)/(i^(2))]` |
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| 25. |
Which of the following sets cannot enter into the list of fundamental quatities in any system of units?A. length , mass and densityB. length , time and velocityC. mass, time and velocityD. length , time and mass |
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Answer» Correct Answer - B In option (b) , all three are related to each other . |
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| 26. |
A force is given by `F= at + bt^(2) ` where , t is the time .The dimensione of a and b areA. `[MLT^(-4)]` and` [MLT]`B. `[MLT^(-1)]` and `[MLT^(0)]`C. `[MLT^(-3)] `and` [MLT^(-4)]`D. `[MLT^(-3)] `and` [MLT^(0)]` |
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Answer» Correct Answer - C ` a = (F)/(t)` `b = (F)/(t^(2)` |
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