02. Dimensions of Physical Quantities and Its Applications
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Units and Measurements

139518 If velocity \((\mathrm{V})\), acceleration \((\mathrm{A})\) and force \((\mathrm{F})\) are considered as fundamental units then the dimension of Young's modulus will be

1 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-5}\right]\)
2 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-4}\right]\)
3 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-3}\right]\)
4 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{2}\right]\)
Tripura-27.04.2022
Units and Measurements

139519 Dimensional formula of electric flux

1 \(\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
2 \(\left[\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{3} \mathrm{~A}^{-1}\right]\)
3 \(\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
4 \(\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
GUJCET 18.04.2022
Units and Measurements

139522 If the velocity of light \(C\), the gravitational constant \(\mathbf{G}\) and Planck's constant \(h\) are chosen as the fundamental units, the dimension of density in the new system is

1 \(\left[\mathrm{C}^{3} \mathrm{G}^{-2} \mathrm{~h}^{1}\right]\)
2 \(\left[\mathrm{C}^{5} \mathrm{G}^{-2} \mathrm{~h}^{-1}\right]\)
3 \(\left[\mathrm{C}^{-3 / 2} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}\right]\)
4 \(\left[\mathrm{C}^{9 / 2} \mathrm{G}^{-1 / 2} \mathrm{~h}^{-1 / 2}\right]\)
TS EAMCET 20.07.2022
Units and Measurements

139523 Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is \(\rho\) and radius of the drop is \(r\), then \(T=K \sqrt{\rho r^{3} / S^{\frac{3}{2}}}\) is dimensionally correct, where \(K\) is dimensionless
Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

1 Both (A) and (R) are true and (R) is the correct explanation of \((\mathrm{A})\)
2 Both (A) and (R) are true but (R) is not the correct explanation of (A)
3 (A) is true but (R) is false
4 (A) is false but (R) is true
JEE Main-29.07.2022
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Units and Measurements

139518 If velocity \((\mathrm{V})\), acceleration \((\mathrm{A})\) and force \((\mathrm{F})\) are considered as fundamental units then the dimension of Young's modulus will be

1 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-5}\right]\)
2 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-4}\right]\)
3 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-3}\right]\)
4 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{2}\right]\)
Tripura-27.04.2022
Units and Measurements

139519 Dimensional formula of electric flux

1 \(\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
2 \(\left[\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{3} \mathrm{~A}^{-1}\right]\)
3 \(\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
4 \(\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
GUJCET 18.04.2022
Units and Measurements

139522 If the velocity of light \(C\), the gravitational constant \(\mathbf{G}\) and Planck's constant \(h\) are chosen as the fundamental units, the dimension of density in the new system is

1 \(\left[\mathrm{C}^{3} \mathrm{G}^{-2} \mathrm{~h}^{1}\right]\)
2 \(\left[\mathrm{C}^{5} \mathrm{G}^{-2} \mathrm{~h}^{-1}\right]\)
3 \(\left[\mathrm{C}^{-3 / 2} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}\right]\)
4 \(\left[\mathrm{C}^{9 / 2} \mathrm{G}^{-1 / 2} \mathrm{~h}^{-1 / 2}\right]\)
TS EAMCET 20.07.2022
Units and Measurements

139523 Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is \(\rho\) and radius of the drop is \(r\), then \(T=K \sqrt{\rho r^{3} / S^{\frac{3}{2}}}\) is dimensionally correct, where \(K\) is dimensionless
Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

1 Both (A) and (R) are true and (R) is the correct explanation of \((\mathrm{A})\)
2 Both (A) and (R) are true but (R) is not the correct explanation of (A)
3 (A) is true but (R) is false
4 (A) is false but (R) is true
JEE Main-29.07.2022
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Units and Measurements

139518 If velocity \((\mathrm{V})\), acceleration \((\mathrm{A})\) and force \((\mathrm{F})\) are considered as fundamental units then the dimension of Young's modulus will be

1 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-5}\right]\)
2 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-4}\right]\)
3 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-3}\right]\)
4 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{2}\right]\)
Tripura-27.04.2022
Units and Measurements

139519 Dimensional formula of electric flux

1 \(\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
2 \(\left[\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{3} \mathrm{~A}^{-1}\right]\)
3 \(\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
4 \(\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
GUJCET 18.04.2022
Units and Measurements

139522 If the velocity of light \(C\), the gravitational constant \(\mathbf{G}\) and Planck's constant \(h\) are chosen as the fundamental units, the dimension of density in the new system is

1 \(\left[\mathrm{C}^{3} \mathrm{G}^{-2} \mathrm{~h}^{1}\right]\)
2 \(\left[\mathrm{C}^{5} \mathrm{G}^{-2} \mathrm{~h}^{-1}\right]\)
3 \(\left[\mathrm{C}^{-3 / 2} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}\right]\)
4 \(\left[\mathrm{C}^{9 / 2} \mathrm{G}^{-1 / 2} \mathrm{~h}^{-1 / 2}\right]\)
TS EAMCET 20.07.2022
Units and Measurements

139523 Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is \(\rho\) and radius of the drop is \(r\), then \(T=K \sqrt{\rho r^{3} / S^{\frac{3}{2}}}\) is dimensionally correct, where \(K\) is dimensionless
Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

1 Both (A) and (R) are true and (R) is the correct explanation of \((\mathrm{A})\)
2 Both (A) and (R) are true but (R) is not the correct explanation of (A)
3 (A) is true but (R) is false
4 (A) is false but (R) is true
JEE Main-29.07.2022
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Units and Measurements

139518 If velocity \((\mathrm{V})\), acceleration \((\mathrm{A})\) and force \((\mathrm{F})\) are considered as fundamental units then the dimension of Young's modulus will be

1 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-5}\right]\)
2 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-4}\right]\)
3 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{-3}\right]\)
4 \(\left[\mathrm{FA}^{2} \mathrm{~V}^{2}\right]\)
Tripura-27.04.2022
Units and Measurements

139519 Dimensional formula of electric flux

1 \(\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
2 \(\left[\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{3} \mathrm{~A}^{-1}\right]\)
3 \(\left[\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
4 \(\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\)
GUJCET 18.04.2022
Units and Measurements

139522 If the velocity of light \(C\), the gravitational constant \(\mathbf{G}\) and Planck's constant \(h\) are chosen as the fundamental units, the dimension of density in the new system is

1 \(\left[\mathrm{C}^{3} \mathrm{G}^{-2} \mathrm{~h}^{1}\right]\)
2 \(\left[\mathrm{C}^{5} \mathrm{G}^{-2} \mathrm{~h}^{-1}\right]\)
3 \(\left[\mathrm{C}^{-3 / 2} \mathrm{G}^{-1 / 2} \mathrm{~h}^{1 / 2}\right]\)
4 \(\left[\mathrm{C}^{9 / 2} \mathrm{G}^{-1 / 2} \mathrm{~h}^{-1 / 2}\right]\)
TS EAMCET 20.07.2022
Units and Measurements

139523 Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is \(\rho\) and radius of the drop is \(r\), then \(T=K \sqrt{\rho r^{3} / S^{\frac{3}{2}}}\) is dimensionally correct, where \(K\) is dimensionless
Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

1 Both (A) and (R) are true and (R) is the correct explanation of \((\mathrm{A})\)
2 Both (A) and (R) are true but (R) is not the correct explanation of (A)
3 (A) is true but (R) is false
4 (A) is false but (R) is true
JEE Main-29.07.2022