Units and Measurements Test

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Units and Measurements Test - 78

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Question 1
1 / -0

The dimensional formula of pressure is

A
$$ [MLT^{-2} ] $$

B
$$ [ML^2T^{-2} ] $$

C
$$ [ML^{-1}T^{-2} ] $$

D
$$ [M^0L^{-1}T^{-2} ] $$

Solution

$$Pressure (P) = \dfrac{Force }{ Area}$$ . . . . . (1)
Since, $$Force = Mass \times Acceleration$$
And, $$Acceleration = \dfrac{Velocity}{Time} =\dfrac{[LT^{-1}]}{[T]}=[LT^{-2}]$$
$$\therefore$$ The dimensional formula of force $$=[M][LT^{-2}]=[MLT^{-2}]$$ . . . . (2)
The dimensional formula of area is $$[M^0L^2T^0]$$ . . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
$$Pressure (P) = \dfrac{Force }{ Area}$$
Or,
$$P=\dfrac{[MLT^{-2}]}{[L^2]}=ML^{-1}T^{-2}$$
Therefore, the pressure is dimensionally represented as $$[ML^{-1}T^{-2}]$$
Question 2
1 / -0

The dimensional formula for the magnetic fields is

A
$$ [MT^{-2} A^{-1} ] $$

B
$$ [ML^2T^{-1}A^{-2} ] $$

C
$$ [MT^{-2}A^{-2}] $$

D
$$ [MT^{-1} A^{-2}] $$

Solution

We have the equation,

$$F=qvB\,sin\theta$$

Dimension of Force, $$F=[MLT^{-2}]$$

Dimension of Velocity, $$v=[LT^{-1}]$$

Dimension of Charge, $$q=[AT]$$

$$Sin\theta $$ is dimensionless

Then,

Magnetic Field, $$B=\dfrac{Force}{Velocity \times Charge}=\dfrac{[MLT^{-2}]}{[LT^{-1}][AT]}=[MT^{-2}A^{-1}]$$
Question 3
1 / -0

The radius of nucleus is $$r = r_0 A^{{1}/{3}}$$, where $$A$$ is mass number. The dimensions of $$r_0$$ is

A
$$[MLT^{-2}]$$

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

C
$$[M^0 L T^0]$$

D
None of these

Solution
Question 4
1 / -0

Dimensional formula of modulus of elasticity is

A
$$\left[ M ^ { 0 } L ^ { - 1 } T ^ { - 2 } \right]$$

B
$$\left[ M ^ { 1 } L ^ { - 1 } T ^ { - 2 } \right]$$

C
$$\left[ M ^ { 1 } L ^ { 1 } T ^ { - 2 } \right]$$

D
$$\left[ M ^ { -1 } L ^ { - 1 } T ^ { - 2 } \right]$$

Solution
Question 5
1 / -0

Given $$x = a + b t + c t ^ { 2 }$$ where $$x$$ in metre and $$t$$ in second. Find the dimensional formula of $$b$$

A
$$L$$

B
$$L T ^ { - 1 }$$

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

D
$$L ^ { 2 }$$

Solution
Question 6
1 / -0

Given $$x = a + b t + c t ^ { 2 }$$ where $$x$$ in metre and $$t$$ in second. Find the dimensional formula of $$C$$

A
$$L$$

B
$$L T ^ { - 1 }$$

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

D
$$L ^ { 2 } T ^ { 2 }$$

Solution
Question 7
1 / -0

If C be the capacitance and V be the electric potential,then the dimensional formula of $$ CV^2 $$ is

A
$$ [ML ^{-3} TA] $$

B
$$ [M^oLT^{-2} A^o] $$

C
$$ [ML ^1 A^{-1 }] $$

D
$$ [ML^2T^{-2} A^o] $$

Solution
Question 8
1 / -0

Given that m is the mass suspended from a spring force constant k. The dimension of the formula for $$\sqrt{m/k}$$ is same as that for

A
frequency

B
time period

C
velocity

D
wavelength

Solution
Question 9
1 / -0

If L be the inductance, R resistance and C be the capacitance of a capacitor, then dimensional formula of $$ \cfrac {L}{R} $$ and RC are

A
$$ M^oLT^{-1}ML ^oT^{-1} $$

B
$$ M^oL^oT,MLT^o $$

C
$$ M^oL^oT, 1 $$

D
$$ M^oL^oT, M^oL^oT $$
Question 10
1 / -0

The dimensions of $$(\mu_{0}\epsilon_{0})^{-\dfrac {1}{2}}$$ are

A
$$[L^{-\dfrac {1}{2}} T^{\dfrac {1}{2}}]$$

B
$$[L^{\dfrac {1}{2}} T^-{\dfrac {1}{2}}]$$

C
$$[L^{-1} T]$$

D
$$[L T^{-1}]$$