Units and Measurements Test

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Units and Measurements Test - 83

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Weekly Quiz Competition

Question 1
1 / -0

Accuracy of measurement is determined by

A
Absolute error

B
Percentage error

C
Both

D
None of these

Solution

Accuracy of measurement is determined by the absolute error. Absolute error is the is the difference between the actual and measured value. It is the maximum possible error that needs to be eliminate to get an accurate measurement.
Question 2
1 / -0

The dimension of $$\dfrac{R}{L}$$ are

A
$$T^2$$

B
$$T$$

C
$$T^{-1}$$

D
$$T^{-2}$$

Solution
Question 3
1 / -0

What is the number of significant figures in $$0.310\times10^3$$

A
2

B
3

C
4

D
6

Solution
Question 4
1 / -0

Pressure gradient has the same dimension as that of

A
Velocity gradient

B
Potential gradient

C
Energy gradient

D
None of these

Solution
Question 5
1 / -0

Which of the following group have different dimension

A
Potential difference, EMF, voltage

B
Pressure, stress, young's modulus

C
Heat, energy, work-done

D
Dipole moment, electric flux, electric field

Solution

Dipole moment = charge x distance
Electric flux = electric field x area
$∴$ Dipole moment, electric flux and electric field have different dimensions.
Question 6
1 / -0

The dimensions of shear modulus are

A
$$MLT^{-1}$$

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

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

D
$$MLT^{-2}$$

Solution
Question 7
1 / -0

The dimensions of magnetic field intensity in $$ M, L , T $$ and $$ C $$ is given as

A
$$ MT^2 C^{-1} $$

B
$$ MLT^{-1}C^{-1} $$

C
$$ MT^2C^{-2} $$

D
$$ MT^{-1}C^{-1} $$

Solution

The dimensions of magnetic field intensity in $$ M, L , T $$ and $$ C $$ is given as $$ MT^{-1}C^{-1} $$
Question 8
1 / -0

Which of the following is the best estimate for the mass of all the people living on the Earth?

A
$$2*10^{8}kg$$

B
$$1*10^{9}kg$$

C
$$2*10^{10}kg$$

D
$$3*10^{11}kg$$

E
$$4*10^{12}kg$$

Solution

The population is about $$6$$ billion = $$6 * 10^{9}$$. Assuming about $$100$$ lb per person = about $$50$$ kg per person ($$1$$ kg has the weight of about $$2.2$$ lb), the total mass is about $$(6 * 10^{9})(50 kg) = 3 * 10^{11} kg$$,
answer (d).
Question 9
1 / -0

An unknown quantity $$\displaystyle "\alpha"$$ is expressed $$\displaystyle \alpha =\frac{2ma}{\beta }\log \left ( 1+\frac{2\beta \varphi }{ma} \right )$$
where $$m$$ = mass, $$a$$ = acceleration, $$\displaystyle \varphi $$ = length
The unit of $$\displaystyle \alpha $$ should be

A
meter

B
$$m/s$$

C
$$m/s$$$$\displaystyle ^{2}$$

D
$$s$$$$\displaystyle ^{-1}$$

Solution

$$\alpha =\dfrac { 2ma }{ \beta } \log { 1+\dfrac { 2\beta \psi }{ ma } } $$

First find unit of $$\beta $$.

The value of log is dimensionless so dimension of:

$$\beta \psi =ma$$

$$\beta (m)=(kg)(m/sec^2)$$

Unit of $$\beta =\dfrac { kg }{ { sec }^{ 2 } } $$

Unit of $$\alpha =\dfrac { kg.m/{ sec }^{ 2 } }{ kg/{ sec }^{ 2 } } =m= meter$$
Question 10
1 / -0

The Bernoulli's equation is given by $$\displaystyle p + \frac {1} {2} \rho v^2 + h \rho g = k $$,
where $$p$$ = pressure, $$ \rho $$ = density, $$v$$ = speed, $$h$$= height of the liquid column,$$g$$ = acceleration due to gravity and $$k$$ is constant. The dimensional formula for $$k$$ is same as that for :

A
Velocity gradient

B
Pressure gradient

C
Modulus of elasticity

D
Thrust

Solution

Dimension of k must be same as pressure according to principle of dimensional homogeneity.
Thus it's dimensions are $$ML^{-1}T^{-2}$$ which is the same as modulus of elasticity (Stress/Strain).

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Units and Measurements Test - 83

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Units and Measurements Test - 83

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Question 1

Absolute error

Percentage error

Both

None of these

Solution

Question 2

$$T^2$$

$$T$$

$$T^{-1}$$

$$T^{-2}$$

Solution

Question 3

2

3

4

6

Solution

Question 4

Velocity gradient

Potential gradient

Energy gradient

None of these

Solution

Question 5

Potential difference, EMF, voltage

Pressure, stress, young's modulus

Heat, energy, work-done

Dipole moment, electric flux, electric field

Solution

Dipole moment = charge x distanceElectric flux = electric field x area∴ Dipole moment, electric flux and electric field have different dimensions.

Question 6

$$MLT^{-1}$$

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

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

$$MLT^{-2}$$

Solution

Question 7

$$ MT^2 C^{-1} $$

$$ MLT^{-1}C^{-1} $$

$$ MT^2C^{-2} $$

$$ MT^{-1}C^{-1} $$

Solution

Question 8

$$2*10^{8}kg$$

$$1*10^{9}kg$$

$$2*10^{10}kg$$

$$3*10^{11}kg$$

$$4*10^{12}kg$$

Solution

Question 9

meter

$$m/s$$

$$m/s$$$$\displaystyle ^{2}$$

$$s$$$$\displaystyle ^{-1}$$

Solution

Question 10

Velocity gradient

Pressure gradient

Modulus of elasticity

Thrust

Solution

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Dipole moment = charge x distance
Electric flux = electric field x area
$∴$ Dipole moment, electric flux and electric field have different dimensions.