What are the units of K=1/4πε0

(1) C2N–1m–2

(2) Nm2C–2

(3) Nm2C2

(4) Unitless

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The SI unit of surface tension is

(1) Dyne/cm

(2) Newton/cm

(3) Newton/metre

(4) Newton-metre

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E, m, l and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of El2m5G2 are

(1) Angle

(2) Length

(3) Mass

(4) Time

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From the equation tanθ=rgv2, one can obtain the angle of banking θ for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is

(1) Both dimensionally and numerically correct

(2) Neither numerically nor dimensionally correct

(3) Dimensionally correct only

(4) Numerically correct only

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A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity η flowing per second through a tube of radius r and length l and having a pressure difference p across its end, is

(1) V=πpr48ηl

(2) V=πηl8pr4

(3) V=8pηlπr4

(4) V=πpη8lr4

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The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the relation v=at+bt+c; the dimensions of a, b and c are

(1) a=L2,b=T,c=LT2

(2) a=LT2,b=LT,c=L

(3) a=LT2,b=L,c=T

(4) a=L,b=LT,c=T2

Concept Questions :-

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From the dimensional consideration, which of the following equation is correct ?

(1) T=2πR3GM

(2) T=2πGMR3

(3) T=2πGMR2

(4) T=2πR2GM

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The position of a particle at time t is given by the relation l =voα(1-eαt) , where v0 is a constant and α > 0. The dimensions of v0 and α are respectively

(1) M0L1T1 and T–1

(2) M0L1T0 and T–1

(3) M0L1T1 and LT–2

(4) M0L1T1 and T

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The dimensions of ab in the equation P=at2bx, where P is pressure, x is distance and t is time, are 

(1) MT–2

(2) M2LT–3

(3) ML3T–1

(4) LT–3

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Dimensions of 1μ0ε0, where symbols have their usual meaning, are 

(1) [LT–1]

(2) [L–1T]

(3) [L–2T2]

(4) [L2T–2]

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