The dimensional formula for impulse is same as the dimensional formula for 

(1) Momentum

(2) Force

(3) Rate of change of momentum

(4) Torque

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Which of the following is dimensionally correct

(1) Pressure = Energy per unit area

(2) Pressure = Energy per unit volume

(3) Pressure = Force per unit volume

(4) Pressure = Momentum per unit volume per unit time

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Planck's constant has the dimensions (unit) of 

(1) Energy

(2) Linear momentum

(3) Work

(4) Angular momentum

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The equation of state of some gases can be expressed as P+aV2(Vb)=RT. Here P is the pressure, V is the volume, T is the absolute temperature and a, b, R are constants. The dimensions of ‘a’ are 

(1) ML5T2

(2) ML1T2

(3) M0L3T0

(4) M0L6T0

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If V denotes the potential difference across the plates of a capacitor of capacitance C, the dimensions of CV2 are     [Only for Dropper and XII batch]

(1) Not expressible in MLT

(2) MLT2

(3) M2LT1

(4) ML2T2

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If L denotes the inductance of an inductor through which a current i is flowing, the dimensions of Li2 are  

(1) ML2T2

(2) Not expressible in MLT

(3) MLT2

(4) LT

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Of the following quantities, which one has dimensions different from the remaining three 

(1) Energy per unit volume

(2) Force per unit area

(3) Product of voltage and charge per unit volume

(4) Angular momentum per unit mass

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A spherical body of mass m and radius r is allowed to fall in a medium of viscosity η. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant (τ). Dimensionally τ can be represented by 

(1) mr26πη

(b) 6πmrηg2

(c) m6πηrv

(4) None of the above

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The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f=CmxKy; where C is a dimensionless quantity. The value of x and y are 

(1) x=12,y=12

(2) x=12,y=12

(3) x=12,y=12

(4) x=12,y=12

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The quantities A and B are related by the relation, m = A/B, where m is the linear density and A is the force. The dimensions of B are of

(1) Pressure

(2) Work

(3) Latent heat

(4) None of the above

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