Units and Measurements Test

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Units and Measurements Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

If the force is given by $$ F$$ = $$at+bt^2$$ with $$ t $$ as time. The dimensions of a and b are:

A
$$[MLT^{-4}], [MLT^{-2}]$$

B
$$[MLT^{-3}], [MLT^{-4}]$$

C
$$[ML^2T^{-3}], [ML^2T^{-2}]$$

D
$$[ML^2T^{-3}], [ML^3T^{-4}]$$

Solution

Dimension of force F : $$[MLT^{-2}]$$
$$F=at+bt^2$$
$$\implies $$ Dimension of $$a:[MLT^{-2}]\times [T^{-1}]$$$$=[MLT^{-3}]$$
Dimensions of $$b:[MLT^{-2}]\times [T^{-2}]$$$$=[MLT^{-4}]$$
Question 2
1 / -0

The dimensional formula for inductance is:

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

B
$$[M^1L^{2}TA^{-2}]$$

C
$$[M^1L^2T^{-1}A^{-2}]$$

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

Solution
Question 3
1 / -0

Linear momentum and angular momentum have the same dimensions in:

A
mass and length

B
length and time

C
mass and time

D
mass, length and time

Solution

Linear momentum $$= mv = [M^{1}L^{1}T^{-1}]$$
Angular momentum $$= mvr = [M^{1}L^{2}T^{-1}]$$
Hence, linear and angular momenta have same dimensions in mass and time.
Question 4
1 / -0

Which of the following does not give the unit of energy ?

A
Watt second

B
Kilowatt hour

C
Newton meter

D
Pascal metre

Solution

Energy $$= M^{1} L^{2} T^{-2}$$
Watt second $$= M^{1} L^{2} T^{-3}\times T = M^{1} L^{2} T^{-2}$$
Kilowatt hr $$= M^{1} L^{2} T^{-3}\times T^{1} = M^{1} L^{2} T^{-2}$$
Newton mt $$= M^{1} L^{1} T^{-2}\times L^{1} = M^{1} L^{2} T^{-2}$$
Pascal mt $$= M^{1} L^{-1} T^{-2}\times L^{1} = M^{1} L^{0} T^{-2}$$
Hence, option D is correct.
Question 5
1 / -0

Magnetic flux and magnetic induction differ in the dimensions of:

A
mass

B
length

C
time

D
all of these

Solution

Magnetic flux = Magnetic Induction $$\times $$ Area $$=[ ML^{2}I^{-1}T^{-2}]$$
Magnetic Induction field strength $$= [MI^{-1}T^{-2}]$$
Hence, dimensions differ in length.
Question 6
1 / -0

The dimensional formula for potential energy is:

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

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

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

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

Solution

Potential energy $$ = [ mgh] \\= [(M^{1}) (LT^{-2}) (L)]$$
$$ = [ML^{2}T^{-2}]$$
Question 7
1 / -0

The mathematical operation in which the accuracy is limited to least accurate term is :

A
addition

B
subtraction

C
multiplication and division

D
both A and B

Solution

In addition or subtraction we can reduce the terms to least accurate term and add or subtract them. By this process in addition or subtraction answer is not much get affected or change in answer is negligible.
But if we apply this process in multiplication and division, change in answer is considerable.
Hence in addition and subtraction accuracy is limited to least accurate term.
Question 8
1 / -0

The SI unit of a physical quantity is [$$Jm^{-2}$$]. The dimensional formula for that quantity is:

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

B
$$M^{1}L^{0}T^{-2}$$

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

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

Solution

$$[Jm^{-2}] = [\dfrac{M^{1}L^{2}T^{-2}}{L^{2}}] = [M^{1}L^{0}T^{-2}]$$
Question 9
1 / -0

Impulse and angular velocity have the same dimensions in

A
mass

B
length

C
time

D
mass, length and time

Solution

Impulse $$ = F\times t = [M^{1}L^{1}T^{-2} \times T^{1}] = [M^{1}L^{1}T^{-1}]$$
Angular velocity $$ = \omega = [M^{0}L^{0}T^{-1}]$$
Hence, time has the same dimension in both the quantities.
Question 10
1 / -0

The dimensional formula for magnetic moment of a magnet is :

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

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

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

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

Solution

We know that magnetic moment for a solenoid is NIS, where N is number of loops, I is current and S is the vector area.
Thus, dimensions of $$\mu$$ are $$[AL^2]=[M^0L^2T^0A]$$

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Units and Measurements Test - 19

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Units and Measurements Test - 19

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Question 1

$$[MLT^{-4}], [MLT^{-2}]$$

$$[MLT^{-3}], [MLT^{-4}]$$

$$[ML^2T^{-3}], [ML^2T^{-2}]$$

$$[ML^2T^{-3}], [ML^3T^{-4}]$$

Solution

Question 2

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

$$[M^1L^{2}TA^{-2}]$$

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

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

Solution

Question 3

mass and length

length and time

mass and time

mass, length and time

Solution

Question 4

Watt second

Kilowatt hour

Newton meter

Pascal metre

Solution

Question 5

mass

length

time

all of these

Solution

Question 6

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

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

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

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

Solution

Question 7

addition

subtraction

multiplication and division

both A and B

Solution

Question 8

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

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

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

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

Solution

Question 9

mass

length

time

mass, length and time

Solution

Question 10

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

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

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

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

Solution

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