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PHXI02:UNITS AND MEASUREMENTS

367255 If the capacitance of a nanocapacitor is measured in terms of a unit '\(u\)' made by combining the electric charge '\(e\)', Bohr radius ' \(a_{0}\) ', Planck's constant ' \(h\) ' and speed of light ' \(c\) ' then:

1 \(u=\dfrac{h c}{e^{2} a_{0}}\)
2 \(u=\dfrac{e^{2} h}{a_{0}}\)
3 \(u=\dfrac{e^{2} a_{0}}{h c}\)
4 \(u=\dfrac{e^{2} c}{h a_{0}}\)
JEE - 2015
PHXI02:UNITS AND MEASUREMENTS

367256 Dimensional formula of ‘\(ohm\)’ is same as

1 \(\frac{h}{e}\)
2 \(\frac{{{h^2}}}{e}\)
3 \(\frac{h}{{{e^2}}}\)
4 \(\frac{{{h^2}}}{{{e^2}}}\)
PHXI02:UNITS AND MEASUREMENTS

367257 The speed of a wave produced in water is given by \(v=\lambda^{a} g^{b} \rho^{c}\). Where \(\lambda, g\) and \(\rho\) are wavelength of wave, acceleration due to gravity and density of water respectively. The values of \(a, b\) and \(c\) respectively, are

1 \(\dfrac{1}{2}, 0, \dfrac{1}{2}\)
2 \(1,-1,0\)
3 \(1,1,0\)
4 \(\dfrac{1}{2}, \dfrac{1}{2}, 0\)
JEE - 2023
PHXI02:UNITS AND MEASUREMENTS

367258 The frequency of vibration of a string is given by \({v=\dfrac{p}{2 l}\left[\dfrac{F}{m}\right]^{1 / 2}}\) Here, \({p}\) is the number of segments in which the string is divided, \({F}\) is the tension in the string, and \({l}\) is its length. The dimensional formula for \({m}\) is

1 \({\left[M^{0} L^{0} T^{0}\right]}\)
2 \({\left[M L^{-1} T^{0}\right]}\)
3 \({\left[M L^{0} T^{-1}\right]}\)
4 \({\left[M^{0} L T^{-1}\right]}\)
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PHXI02:UNITS AND MEASUREMENTS

367255 If the capacitance of a nanocapacitor is measured in terms of a unit '\(u\)' made by combining the electric charge '\(e\)', Bohr radius ' \(a_{0}\) ', Planck's constant ' \(h\) ' and speed of light ' \(c\) ' then:

1 \(u=\dfrac{h c}{e^{2} a_{0}}\)
2 \(u=\dfrac{e^{2} h}{a_{0}}\)
3 \(u=\dfrac{e^{2} a_{0}}{h c}\)
4 \(u=\dfrac{e^{2} c}{h a_{0}}\)
JEE - 2015
PHXI02:UNITS AND MEASUREMENTS

367256 Dimensional formula of ‘\(ohm\)’ is same as

1 \(\frac{h}{e}\)
2 \(\frac{{{h^2}}}{e}\)
3 \(\frac{h}{{{e^2}}}\)
4 \(\frac{{{h^2}}}{{{e^2}}}\)
PHXI02:UNITS AND MEASUREMENTS

367257 The speed of a wave produced in water is given by \(v=\lambda^{a} g^{b} \rho^{c}\). Where \(\lambda, g\) and \(\rho\) are wavelength of wave, acceleration due to gravity and density of water respectively. The values of \(a, b\) and \(c\) respectively, are

1 \(\dfrac{1}{2}, 0, \dfrac{1}{2}\)
2 \(1,-1,0\)
3 \(1,1,0\)
4 \(\dfrac{1}{2}, \dfrac{1}{2}, 0\)
JEE - 2023
PHXI02:UNITS AND MEASUREMENTS

367258 The frequency of vibration of a string is given by \({v=\dfrac{p}{2 l}\left[\dfrac{F}{m}\right]^{1 / 2}}\) Here, \({p}\) is the number of segments in which the string is divided, \({F}\) is the tension in the string, and \({l}\) is its length. The dimensional formula for \({m}\) is

1 \({\left[M^{0} L^{0} T^{0}\right]}\)
2 \({\left[M L^{-1} T^{0}\right]}\)
3 \({\left[M L^{0} T^{-1}\right]}\)
4 \({\left[M^{0} L T^{-1}\right]}\)
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PHXI02:UNITS AND MEASUREMENTS

367255 If the capacitance of a nanocapacitor is measured in terms of a unit '\(u\)' made by combining the electric charge '\(e\)', Bohr radius ' \(a_{0}\) ', Planck's constant ' \(h\) ' and speed of light ' \(c\) ' then:

1 \(u=\dfrac{h c}{e^{2} a_{0}}\)
2 \(u=\dfrac{e^{2} h}{a_{0}}\)
3 \(u=\dfrac{e^{2} a_{0}}{h c}\)
4 \(u=\dfrac{e^{2} c}{h a_{0}}\)
JEE - 2015
PHXI02:UNITS AND MEASUREMENTS

367256 Dimensional formula of ‘\(ohm\)’ is same as

1 \(\frac{h}{e}\)
2 \(\frac{{{h^2}}}{e}\)
3 \(\frac{h}{{{e^2}}}\)
4 \(\frac{{{h^2}}}{{{e^2}}}\)
PHXI02:UNITS AND MEASUREMENTS

367257 The speed of a wave produced in water is given by \(v=\lambda^{a} g^{b} \rho^{c}\). Where \(\lambda, g\) and \(\rho\) are wavelength of wave, acceleration due to gravity and density of water respectively. The values of \(a, b\) and \(c\) respectively, are

1 \(\dfrac{1}{2}, 0, \dfrac{1}{2}\)
2 \(1,-1,0\)
3 \(1,1,0\)
4 \(\dfrac{1}{2}, \dfrac{1}{2}, 0\)
JEE - 2023
PHXI02:UNITS AND MEASUREMENTS

367258 The frequency of vibration of a string is given by \({v=\dfrac{p}{2 l}\left[\dfrac{F}{m}\right]^{1 / 2}}\) Here, \({p}\) is the number of segments in which the string is divided, \({F}\) is the tension in the string, and \({l}\) is its length. The dimensional formula for \({m}\) is

1 \({\left[M^{0} L^{0} T^{0}\right]}\)
2 \({\left[M L^{-1} T^{0}\right]}\)
3 \({\left[M L^{0} T^{-1}\right]}\)
4 \({\left[M^{0} L T^{-1}\right]}\)
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PHXI02:UNITS AND MEASUREMENTS

367255 If the capacitance of a nanocapacitor is measured in terms of a unit '\(u\)' made by combining the electric charge '\(e\)', Bohr radius ' \(a_{0}\) ', Planck's constant ' \(h\) ' and speed of light ' \(c\) ' then:

1 \(u=\dfrac{h c}{e^{2} a_{0}}\)
2 \(u=\dfrac{e^{2} h}{a_{0}}\)
3 \(u=\dfrac{e^{2} a_{0}}{h c}\)
4 \(u=\dfrac{e^{2} c}{h a_{0}}\)
JEE - 2015
PHXI02:UNITS AND MEASUREMENTS

367256 Dimensional formula of ‘\(ohm\)’ is same as

1 \(\frac{h}{e}\)
2 \(\frac{{{h^2}}}{e}\)
3 \(\frac{h}{{{e^2}}}\)
4 \(\frac{{{h^2}}}{{{e^2}}}\)
PHXI02:UNITS AND MEASUREMENTS

367257 The speed of a wave produced in water is given by \(v=\lambda^{a} g^{b} \rho^{c}\). Where \(\lambda, g\) and \(\rho\) are wavelength of wave, acceleration due to gravity and density of water respectively. The values of \(a, b\) and \(c\) respectively, are

1 \(\dfrac{1}{2}, 0, \dfrac{1}{2}\)
2 \(1,-1,0\)
3 \(1,1,0\)
4 \(\dfrac{1}{2}, \dfrac{1}{2}, 0\)
JEE - 2023
PHXI02:UNITS AND MEASUREMENTS

367258 The frequency of vibration of a string is given by \({v=\dfrac{p}{2 l}\left[\dfrac{F}{m}\right]^{1 / 2}}\) Here, \({p}\) is the number of segments in which the string is divided, \({F}\) is the tension in the string, and \({l}\) is its length. The dimensional formula for \({m}\) is

1 \({\left[M^{0} L^{0} T^{0}\right]}\)
2 \({\left[M L^{-1} T^{0}\right]}\)
3 \({\left[M L^{0} T^{-1}\right]}\)
4 \({\left[M^{0} L T^{-1}\right]}\)
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