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

(1) Momentum

(2) Force

(3) Rate of change of momentum

(4) Torque

Concept Questions :-

Dimensions
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Difficulty Level:

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

Concept Questions :-

Dimensions
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Difficulty Level:

Planck's constant has the dimensions (unit) of

(1) Energy

(2) Linear momentum

(3) Work

(4) Angular momentum

Concept Questions :-

Dimensions
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Difficulty Level:

The equation of state of some gases can be expressed as $\left(P+\frac{a}{{V}^{2}}\right)\left(V-b\right)=RT$. 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) $M{L}^{5}{T}^{-2}$

(2) $M{L}^{-1}{T}^{-2}$

(3) ${M}^{0}{L}^{3}{T}^{0}$

(4) ${M}^{0}{L}^{6}{T}^{0}$

Concept Questions :-

Dimensions
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Difficulty Level:

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) $ML{T}^{-2}$

(3) ${M}^{2}L{T}^{-1}$

(4) $M{L}^{2}{T}^{-2}$

Concept Questions :-

Dimensions
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Difficulty Level:

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

(1) $M{L}^{2}{T}^{-2}$

(2) Not expressible in MLT

(3) $ML{T}^{-2}$

(4) LT

Concept Questions :-

Dimensions
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Difficulty Level:

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

Concept Questions :-

Dimensions
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Difficulty Level:

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

(1) $\frac{m{r}^{2}}{6\pi \eta }$

(b) $\sqrt{\left(\frac{6\pi mr\eta }{{g}^{2}}\right)}$

(c) $\frac{m}{6\pi \eta rv}$

(4) None of the above

Concept Questions :-

Dimensions
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Difficulty Level:

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 $f=C\text{\hspace{0.17em}}{m}^{x}{K}^{y}$; where C is a dimensionless quantity. The value of x and y are

(1) $x=\frac{1}{2},\text{\hspace{0.17em}}y=\frac{1}{2}$

(2) $x=-\frac{1}{2},\text{\hspace{0.17em}}y=-\frac{1}{2}$

(3) $x=\frac{1}{2},\text{\hspace{0.17em}}y=-\frac{1}{2}$

(4) $x=-\frac{1}{2},\text{\hspace{0.17em}}y=\frac{1}{2}$

Concept Questions :-

Dimensions
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Difficulty Level:

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

Concept Questions :-

Dimensions