139474
Which of the following is the smallest unit?
1 Millimetre
2 Angstrom
3 Fermi
4 Metre
Explanation:
C 1 Fermi \(=10^{-15} \mathrm{~m}\) 1 Angstrom \((\AA)=10^{-10} \mathrm{~m}\) 1 millimeter \(=10^{-3} \mathrm{~m}\) meter is the unit of length So, the smallest unit is Fermi.
UPSEE - 2010
Units and Measurements
139475
Given that : \(y=A \sin \left[\left(\frac{2 \pi}{\lambda}\right)(\operatorname{ct}-x)\right]\) where, \(y\) and \(x\) are measured in metres. Which of the following statements is true?
1 The unit of \(\lambda\) is same as that of \(x\) and \(A\)
2 The unit of \(\lambda\) is same as that of \(x\) but not of A
3 The unit of \(c\) is same as that of \(\frac{2 \pi}{\lambda}\)
4 The unit of \((\mathrm{ct}-\mathrm{x})\) is same as that of \(\frac{2 \pi}{\lambda}\)
Explanation:
A Here, \(\frac{2 \pi}{\lambda}(\mathrm{ct}-\mathrm{x})\) is dimensionless. Hence, \(\frac{c t}{\lambda}\) is also dimensionless and unit of ct is same as that of \(\mathrm{x}\). Therefore, unit of \(\lambda\) is same as that of \(x\). Also limit of \(y\) is same as that of \(\mathrm{A}\), which is also same as unit of \(\mathrm{x}\).
UPSEE - 2006
Units and Measurements
139477
Which is not the unit of electric field?
1 \(\frac{\mathrm{N}}{\mathrm{C}}\)
2 \(\frac{\mathrm{N}-\mathrm{m}}{\mathrm{C}}\)
3 \(\frac{V}{m}\)
4 \(\frac{\mathrm{J}}{\mathrm{C}-\mathrm{m}}\)
Explanation:
B \(\because\) Electric field \((\mathrm{E})=\frac{\text { Force }}{\text { Charge }}=\mathrm{N} /\) coloumb or \(\mathrm{N} / \mathrm{C}\) \(\because\) The relation between an electric field and an electric potential is \(\mathrm{E}=\) Potential \((\mathrm{v}) /\) distance \((\mathrm{r})\) \(\text { unit of E.F. }=\frac{\mathrm{v}}{\mathrm{m}}\) Also, \(\mathrm{E}=\frac{\mathrm{W}}{\mathrm{q} \cdot \mathrm{x}}=\frac{\mathrm{J}}{\mathrm{C}-\mathrm{m}}\)
JCECE-2006
Units and Measurements
139479
If \(\mathrm{e}\) is the charge, \(\mathrm{V}\) the potential difference, \(\mathrm{T}\) the temperature, then the units of \(\frac{\mathrm{eV}}{\mathrm{T}}\) are the same as that of
1 Planck's constant
2 Stefan's constant
3 Boltzmann's constant
4 Gravitational constant
Explanation:
C \(\because \frac{\mathrm{eV}}{\mathrm{T}}=\frac{\text { Work done }(\mathrm{W})}{\mathrm{T}}\) \(=\frac{\mathrm{PV}}{\mathrm{T}} \quad\left(\because \mathrm{PV}=\frac{\mathrm{RT}}{\mathrm{N}}\right)\) \(=\frac{\mathrm{R}}{\mathrm{N}}=\mathrm{K}=\) Boltzmann constant
139474
Which of the following is the smallest unit?
1 Millimetre
2 Angstrom
3 Fermi
4 Metre
Explanation:
C 1 Fermi \(=10^{-15} \mathrm{~m}\) 1 Angstrom \((\AA)=10^{-10} \mathrm{~m}\) 1 millimeter \(=10^{-3} \mathrm{~m}\) meter is the unit of length So, the smallest unit is Fermi.
UPSEE - 2010
Units and Measurements
139475
Given that : \(y=A \sin \left[\left(\frac{2 \pi}{\lambda}\right)(\operatorname{ct}-x)\right]\) where, \(y\) and \(x\) are measured in metres. Which of the following statements is true?
1 The unit of \(\lambda\) is same as that of \(x\) and \(A\)
2 The unit of \(\lambda\) is same as that of \(x\) but not of A
3 The unit of \(c\) is same as that of \(\frac{2 \pi}{\lambda}\)
4 The unit of \((\mathrm{ct}-\mathrm{x})\) is same as that of \(\frac{2 \pi}{\lambda}\)
Explanation:
A Here, \(\frac{2 \pi}{\lambda}(\mathrm{ct}-\mathrm{x})\) is dimensionless. Hence, \(\frac{c t}{\lambda}\) is also dimensionless and unit of ct is same as that of \(\mathrm{x}\). Therefore, unit of \(\lambda\) is same as that of \(x\). Also limit of \(y\) is same as that of \(\mathrm{A}\), which is also same as unit of \(\mathrm{x}\).
UPSEE - 2006
Units and Measurements
139477
Which is not the unit of electric field?
1 \(\frac{\mathrm{N}}{\mathrm{C}}\)
2 \(\frac{\mathrm{N}-\mathrm{m}}{\mathrm{C}}\)
3 \(\frac{V}{m}\)
4 \(\frac{\mathrm{J}}{\mathrm{C}-\mathrm{m}}\)
Explanation:
B \(\because\) Electric field \((\mathrm{E})=\frac{\text { Force }}{\text { Charge }}=\mathrm{N} /\) coloumb or \(\mathrm{N} / \mathrm{C}\) \(\because\) The relation between an electric field and an electric potential is \(\mathrm{E}=\) Potential \((\mathrm{v}) /\) distance \((\mathrm{r})\) \(\text { unit of E.F. }=\frac{\mathrm{v}}{\mathrm{m}}\) Also, \(\mathrm{E}=\frac{\mathrm{W}}{\mathrm{q} \cdot \mathrm{x}}=\frac{\mathrm{J}}{\mathrm{C}-\mathrm{m}}\)
JCECE-2006
Units and Measurements
139479
If \(\mathrm{e}\) is the charge, \(\mathrm{V}\) the potential difference, \(\mathrm{T}\) the temperature, then the units of \(\frac{\mathrm{eV}}{\mathrm{T}}\) are the same as that of
1 Planck's constant
2 Stefan's constant
3 Boltzmann's constant
4 Gravitational constant
Explanation:
C \(\because \frac{\mathrm{eV}}{\mathrm{T}}=\frac{\text { Work done }(\mathrm{W})}{\mathrm{T}}\) \(=\frac{\mathrm{PV}}{\mathrm{T}} \quad\left(\because \mathrm{PV}=\frac{\mathrm{RT}}{\mathrm{N}}\right)\) \(=\frac{\mathrm{R}}{\mathrm{N}}=\mathrm{K}=\) Boltzmann constant
139474
Which of the following is the smallest unit?
1 Millimetre
2 Angstrom
3 Fermi
4 Metre
Explanation:
C 1 Fermi \(=10^{-15} \mathrm{~m}\) 1 Angstrom \((\AA)=10^{-10} \mathrm{~m}\) 1 millimeter \(=10^{-3} \mathrm{~m}\) meter is the unit of length So, the smallest unit is Fermi.
UPSEE - 2010
Units and Measurements
139475
Given that : \(y=A \sin \left[\left(\frac{2 \pi}{\lambda}\right)(\operatorname{ct}-x)\right]\) where, \(y\) and \(x\) are measured in metres. Which of the following statements is true?
1 The unit of \(\lambda\) is same as that of \(x\) and \(A\)
2 The unit of \(\lambda\) is same as that of \(x\) but not of A
3 The unit of \(c\) is same as that of \(\frac{2 \pi}{\lambda}\)
4 The unit of \((\mathrm{ct}-\mathrm{x})\) is same as that of \(\frac{2 \pi}{\lambda}\)
Explanation:
A Here, \(\frac{2 \pi}{\lambda}(\mathrm{ct}-\mathrm{x})\) is dimensionless. Hence, \(\frac{c t}{\lambda}\) is also dimensionless and unit of ct is same as that of \(\mathrm{x}\). Therefore, unit of \(\lambda\) is same as that of \(x\). Also limit of \(y\) is same as that of \(\mathrm{A}\), which is also same as unit of \(\mathrm{x}\).
UPSEE - 2006
Units and Measurements
139477
Which is not the unit of electric field?
1 \(\frac{\mathrm{N}}{\mathrm{C}}\)
2 \(\frac{\mathrm{N}-\mathrm{m}}{\mathrm{C}}\)
3 \(\frac{V}{m}\)
4 \(\frac{\mathrm{J}}{\mathrm{C}-\mathrm{m}}\)
Explanation:
B \(\because\) Electric field \((\mathrm{E})=\frac{\text { Force }}{\text { Charge }}=\mathrm{N} /\) coloumb or \(\mathrm{N} / \mathrm{C}\) \(\because\) The relation between an electric field and an electric potential is \(\mathrm{E}=\) Potential \((\mathrm{v}) /\) distance \((\mathrm{r})\) \(\text { unit of E.F. }=\frac{\mathrm{v}}{\mathrm{m}}\) Also, \(\mathrm{E}=\frac{\mathrm{W}}{\mathrm{q} \cdot \mathrm{x}}=\frac{\mathrm{J}}{\mathrm{C}-\mathrm{m}}\)
JCECE-2006
Units and Measurements
139479
If \(\mathrm{e}\) is the charge, \(\mathrm{V}\) the potential difference, \(\mathrm{T}\) the temperature, then the units of \(\frac{\mathrm{eV}}{\mathrm{T}}\) are the same as that of
1 Planck's constant
2 Stefan's constant
3 Boltzmann's constant
4 Gravitational constant
Explanation:
C \(\because \frac{\mathrm{eV}}{\mathrm{T}}=\frac{\text { Work done }(\mathrm{W})}{\mathrm{T}}\) \(=\frac{\mathrm{PV}}{\mathrm{T}} \quad\left(\because \mathrm{PV}=\frac{\mathrm{RT}}{\mathrm{N}}\right)\) \(=\frac{\mathrm{R}}{\mathrm{N}}=\mathrm{K}=\) Boltzmann constant
139474
Which of the following is the smallest unit?
1 Millimetre
2 Angstrom
3 Fermi
4 Metre
Explanation:
C 1 Fermi \(=10^{-15} \mathrm{~m}\) 1 Angstrom \((\AA)=10^{-10} \mathrm{~m}\) 1 millimeter \(=10^{-3} \mathrm{~m}\) meter is the unit of length So, the smallest unit is Fermi.
UPSEE - 2010
Units and Measurements
139475
Given that : \(y=A \sin \left[\left(\frac{2 \pi}{\lambda}\right)(\operatorname{ct}-x)\right]\) where, \(y\) and \(x\) are measured in metres. Which of the following statements is true?
1 The unit of \(\lambda\) is same as that of \(x\) and \(A\)
2 The unit of \(\lambda\) is same as that of \(x\) but not of A
3 The unit of \(c\) is same as that of \(\frac{2 \pi}{\lambda}\)
4 The unit of \((\mathrm{ct}-\mathrm{x})\) is same as that of \(\frac{2 \pi}{\lambda}\)
Explanation:
A Here, \(\frac{2 \pi}{\lambda}(\mathrm{ct}-\mathrm{x})\) is dimensionless. Hence, \(\frac{c t}{\lambda}\) is also dimensionless and unit of ct is same as that of \(\mathrm{x}\). Therefore, unit of \(\lambda\) is same as that of \(x\). Also limit of \(y\) is same as that of \(\mathrm{A}\), which is also same as unit of \(\mathrm{x}\).
UPSEE - 2006
Units and Measurements
139477
Which is not the unit of electric field?
1 \(\frac{\mathrm{N}}{\mathrm{C}}\)
2 \(\frac{\mathrm{N}-\mathrm{m}}{\mathrm{C}}\)
3 \(\frac{V}{m}\)
4 \(\frac{\mathrm{J}}{\mathrm{C}-\mathrm{m}}\)
Explanation:
B \(\because\) Electric field \((\mathrm{E})=\frac{\text { Force }}{\text { Charge }}=\mathrm{N} /\) coloumb or \(\mathrm{N} / \mathrm{C}\) \(\because\) The relation between an electric field and an electric potential is \(\mathrm{E}=\) Potential \((\mathrm{v}) /\) distance \((\mathrm{r})\) \(\text { unit of E.F. }=\frac{\mathrm{v}}{\mathrm{m}}\) Also, \(\mathrm{E}=\frac{\mathrm{W}}{\mathrm{q} \cdot \mathrm{x}}=\frac{\mathrm{J}}{\mathrm{C}-\mathrm{m}}\)
JCECE-2006
Units and Measurements
139479
If \(\mathrm{e}\) is the charge, \(\mathrm{V}\) the potential difference, \(\mathrm{T}\) the temperature, then the units of \(\frac{\mathrm{eV}}{\mathrm{T}}\) are the same as that of
1 Planck's constant
2 Stefan's constant
3 Boltzmann's constant
4 Gravitational constant
Explanation:
C \(\because \frac{\mathrm{eV}}{\mathrm{T}}=\frac{\text { Work done }(\mathrm{W})}{\mathrm{T}}\) \(=\frac{\mathrm{PV}}{\mathrm{T}} \quad\left(\because \mathrm{PV}=\frac{\mathrm{RT}}{\mathrm{N}}\right)\) \(=\frac{\mathrm{R}}{\mathrm{N}}=\mathrm{K}=\) Boltzmann constant
