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NEET NEET Questions — Free MCQ Practice

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

A.

FT²

B.

$F^{- 1} T^{2}$

C.

$F^{- 1} A^{2} T^{- 1}$

D.

AT²

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Explanation

Acceleration = $\frac{distance}{{time}^{2}}$

$\Rightarrow A = L T^{- 2} \Rightarrow L = A T^{2}$

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

A.

Velocity

B.

Time

C.

Capacitance

D.

Distance

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Explanation

$\frac{1}{\sqrt{ε_{0} μ_{0}}} = C =$ velocity of light

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

A.

$M L T^{- 2}$

B.

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

C.

MLT²

D.

L

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Explanation

According to problem muscle × speed = power

$∴$ muscle = $\frac{power}{speed} = \frac{M L^{2} T^{- 3}}{L T^{- 1}}$ = $M L T^{- 2}$

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The dimensional formula of wave number is

A.

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

B.

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

C.

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

D.

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

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Explanation

Wave number = $\frac{1}{λ}$

$∴$ dimension is $[M^{0} L^{- 1} T^{0}]$

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The dimensions of stress are equal to

A.

Force

B.

Pressure

C.

Work

D.

$\frac{1}{Pressure}$

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Explanation

[Pressure] =[stress] = $[M L^{- 1} T^{- 2}]$

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The dimensions of pressure are

A.

$M L T^{- 2}$

B.

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

C.

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

D.

$M L T^{2}$

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Explanation

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

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Dimensions of permeability are

A.

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

B.

$M L T^{- 2}$

C.

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

D.

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

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Explanation

$F = \frac{μ_{0}}{4 π} \frac{2 I_{1} I_{2} l}{r}$ $\Rightarrow μ_{0} = [F] {[A]}^{- 2} = [M L T^{- 2} A^{- 2}]$

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Dimensional formula of magnetic flux is

A.

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

B.

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

C.

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

D.

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

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Explanation

$φ = B A = \frac{F}{I \times L} A = \frac{[M L T^{- 2}] [L^{2}]}{[A] [L]} = [M L^{2} T^{- 2} A^{- 1}]$

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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

A.

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

B.

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

C.

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

D.

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

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Explanation

By substituting the dimension of given quantities ${[M L^{- 1} T^{- 2}]}^{x} {[M T^{- 3}]}^{y} {[L T^{- 1}]}^{z} = {[M L T]}^{0}$

$x + y = 0 - (i) - x + z = 0 - (ii) - 2 x - 3 y - z = 0 - (iii) We will try to express y and z in terms of x & substitute in (iii) From (i) y = - x From (ii) z = x Also comparing these 2 euqation z = - y Putting in (iii) - 2 x - 3 (- x) - x = 0 3 x - 3 x = 0 0 = 0$

As you can see, in equation (iii) everything is cancelling. We need one more equation to find values. But if one variable is given, others can be found.

$Ex : If x = 1 Then z = 1 and y = - 1 So in Question, if options are, for values of x, y and z (1) 1, 1, - 1 (2) 1, - 1, 1 (3) - 1, 1, 1 (4) 1, 1, 1 Then option (2) is correct .$

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Inductance L can be dimensionally represented as

A.

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

B.

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

C.

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

D.

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

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Explanation

$E = \frac{1}{2} L i^{2}$ hence $L = [M L^{2} T^{- 2} A^{- 2}]$

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