Physics - Units Measurement - Quiz-5

The velocity of water waves v may depend upon their wavelength $λ$ , the density of water $ρ$ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as:

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$v^{2} \propto {gλ}^{- 1} ρ^{- 1}$
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$v^{2} \propto gλρ$
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$v^{2} \propto gλ$
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$v^{2} \propto g^{- 1} λ^{- 3}$

The dimensions of resistivity in terms of M, L, T and Q where Q stands for the dimensions of charge, will be

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$M L^{3} T^{- 1} Q^{- 2}$
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$M L^{3} T^{- 2} Q^{- 1}$
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$M L^{2} T^{- 1} Q^{- 1}$
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$M L T^{- 1} Q^{- 1}$

The dimensions of Farad are , where Q represents electric charge [This question includes concepts from 12th syllabus]

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$M^{- 1} L^{- 2} T^{2} Q^{2}$
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$M^{- 1} L^{- 2} T Q$
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$M^{- 1} L^{- 2} T^{- 2} Q$
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$M^{- 1} L^{- 2} T Q^{2}$

The equation of a wave is given by $Y = A \sin ω (\frac{x}{v} - k)$ where $ω$ is the angular velocity, x is length and $v$ is the linear velocity. The dimension of k is

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LT
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T
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$T^{- 1}$
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T²

Dimensional formula of capacitance is

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$M^{- 1} L^{- 2} T^{4} A^{2}$
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$M L^{2} T^{4} A^{- 2}$
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$M L T^{- 4} A^{2}$
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$M^{- 1} L^{- 2} T^{- 4} A^{- 2}$

Dimensional formula of heat energy is

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$M L^{2} T^{- 2}$
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$M L T^{- 1}$
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$M^{0} L^{0} T^{- 2}$
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None of these

If C and L denote capacitance and inductance respectively, then the dimensions of LC are

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$M^{0} L^{0} T^{0}$
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$M^{0} L^{0} T^{2}$
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$M^{2} L^{0} T^{2}$
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$M L T^{2}$

Which of the following quantities has the same dimensions as that of energy?

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Power
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Force
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Momentum
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Work

If 97.52 is divided by 2.54, the correct result in terms of significant figures is:

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38.4
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38.3937
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38.394
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38.39

The dimensions of "time constant" $\frac{L}{R}$ during growth and decay of current in all inductive circuit is same as that of

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Constant
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Resistance
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Current
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Time

The period of a body under SHM is presented by $T = P^{a} D^{b} S^{c}$ ; where P is pressure, D is density and S is surface tension. The value of a, b and c are:

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$- \frac{3}{2}, \frac{1}{2}, 1$
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$- 1, - 2, 3$
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$\frac{1}{2}, - \frac{3}{2}, - \frac{1}{2}$
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$1, 2, \frac{1}{3}$

Which of the following pairs of physical quantities has the same dimensions

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Work and power
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Momentum and energy
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Force and power
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Work and energy

The velocity of a freely falling body changes according to $g^{p} h^{q}$ where g is acceleration due to gravity and h is the height. The values of p and q are:

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$1, \frac{1}{2}$
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$\frac{1}{2}, \frac{1}{2}$
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$\frac{1}{2}, 1$
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1, 1

Which one of the following does not have the same dimensions

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Work and energy
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Angle and strain
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Relative density and refractive index
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Planck constant and energy

Which one has the dimensions different from the remaining three

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Power
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Work
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Torque
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Energy

A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $η$ . After some time the velocity of the ball attains a constant value known as terminal velocity $v_{T}$ . The terminal velocity depends on (i) the mass of the ball m, (ii) $η$ , (iii) r and (iv) acceleration due to gravity g. Which of the following relations is dimensionally correct?

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$v_{T} \propto \frac{m g}{η r}$
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$v_{T} \propto \frac{η r}{m g}$
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$v_{T} \propto η r m g$
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$v_{T} \propto \frac{m g r}{η}$

The quantity $X = \frac{ε_{0} L V}{t}; ε_{0}$ is the permittivity of free space, L is length, V is the potential difference and t is time. The dimensions of X are the same as that of:

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Resistance
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Charge
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Voltage
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Current

$μ_{0}$ and $ε_{0}$ denote the permeability and permittivity of free space, the dimensions of $μ_{0} ε_{0}$ are:

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$L T^{- 1}$
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$L^{- 2} T^{2}$
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$M^{- 1} L^{- 3} Q^{2} T^{2}$
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$M^{- 1} L^{- 3} I^{2} T^{2}$

The expression $[M L^{2} T^{- 2}]$ represents

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Pressure
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Kinetic energy
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Momentum
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Power

The dimensions of physical quantity X in the equation Force $= \frac{X}{Density}$ is given by

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$M^{1} L^{4} T^{- 2}$
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$M^{2} L^{- 2} T^{- 1}$
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$M^{2} L^{- 2} T^{- 2}$
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$M^{1} L^{- 2} T^{- 1}$

The dimensions of CV² matches with the dimensions of

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L²I
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L²I ²
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LI²
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$\frac{1}{L I}$

The Martians use force (F), acceleration (A) and time (T) as their fundamental physical quantities. The dimensions of length on Martians system are

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[FT²]
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[ $F^{- 1} T^{2}$ ]
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[ $F^{- 1} A^{2} T^{- 1}$ ]
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[AT²]

The dimension of $\frac{1}{\sqrt{ε_{0} μ_{0}}}$ is that of

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Velocity
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Time
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Capacitance
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Distance

An athletic coach told his team that muscle times speed equals power. What dimensions does he view for muscle?

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$M L T^{- 2}$
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$M L^{2} T^{- 2}$
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MLT²
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L

The dimensional formula of wave number is

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$M^{0} L^{0} T^{- 1}$
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$M^{0} L^{- 1} T^{0}$
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$M^{- 1} L^{- 1} T^{0}$
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$M^{0} L^{0} T^{0}$

The dimensions of stress are equal to

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Force
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Pressure
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Work
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$\frac{1}{Pressure}$

Dimensional formula of magnetic flux is

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$M L^{2} T^{- 2} A^{- 1}$
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$M L^{0} T^{- 2} A^{- 2}$
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$M^{0} L^{- 2} T^{- 2} A^{- 3}$
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$M L^{2} T^{- 2} A^{3}$

If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, then non-zero integers x, y and z such that $P^{x} Q^{y} c^{z}$ is dimensionless, are

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$x = 1, y = 1, z = - 1$
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$x = 1, y = - 1, z = 1$
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$x = - 1, y = 1, z = 1$
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$x = 1, y = 1, z = 1$

Inductance L can be dimensionally represented as

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$M L^{2} T^{- 2} A^{- 2}$
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$M L^{2} T^{- 4} A^{- 3}$
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$M L^{- 2} T^{- 2} A^{- 2}$
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$M L^{2} T^{4} A^{3}$

Dimensions of kinetic energy are

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

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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