367336
In the relation: \(\dfrac{d y}{d t}=2 \omega \sin \left(\omega t+\phi_{0}\right)\), the dimensional formula for \(\left(\omega t+\phi_{0}\right)\) is:
1 \([M L T]\)
2 \(\left[M L T^{0}\right]\)
3 \(\left[M L^{0} T^{0}\right]\)
4 \(\left[M^{0} L^{0} T^{0}\right]\)
Explanation:
Here, \(\left(\omega t+\phi_{0}\right)\) is dimensionless because it is an argument of a trigonometric function. Correct option is (4).
PHXI02:UNITS AND MEASUREMENTS
367337
If \(I=a\left(1-e^{\frac{t}{\lambda}}\right)\), then (where, \(I\) is electric current and \(t\) is time).
1 the SI unit of \(a\) is coulomb
2 the SI unit of \(\lambda\) is per second
3 \(e^{\frac{t}{\lambda}}\) is unitless
4 the SI unit of \(a e^{\frac{t}{\lambda}}\) is ampere per second
Explanation:
\(I=a\left(1-e^{\frac{-t}{\lambda}}\right)\) Here, unit of \(I=\) unit of \(a=\) unit of \(a e^{\frac{-t}{\lambda}}\).
PHXI02:UNITS AND MEASUREMENTS
367338
Suppose refractive index \(\mu\) is given as \(\mu=A+B / \lambda^{2}\), where \(A\) and \(B\) are constants and \(\lambda\) is wavelength, then the dimension of \(B\) is same as that of
1 wavelength
2 pressure
3 area
4 volume
Explanation:
As, \(\mu=\dfrac{\text { Velocity of light in vaccum }}{\text { Velocity of light in medium }}\) The refractive index \(\mu\) is dimensionless, so each term on right hand side is dimensionless Hence, \(\dfrac{B}{\lambda^{2}}\) is also dimensionless. This implies that dimensions of \(B\) will have the dimensions of \(\lambda^{2}\), \(i.e\) of area.
PHXI02:UNITS AND MEASUREMENTS
367339
Which equation is dimensionally incorrect, where symbol represent their usual meaning?
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PHXI02:UNITS AND MEASUREMENTS
367336
In the relation: \(\dfrac{d y}{d t}=2 \omega \sin \left(\omega t+\phi_{0}\right)\), the dimensional formula for \(\left(\omega t+\phi_{0}\right)\) is:
1 \([M L T]\)
2 \(\left[M L T^{0}\right]\)
3 \(\left[M L^{0} T^{0}\right]\)
4 \(\left[M^{0} L^{0} T^{0}\right]\)
Explanation:
Here, \(\left(\omega t+\phi_{0}\right)\) is dimensionless because it is an argument of a trigonometric function. Correct option is (4).
PHXI02:UNITS AND MEASUREMENTS
367337
If \(I=a\left(1-e^{\frac{t}{\lambda}}\right)\), then (where, \(I\) is electric current and \(t\) is time).
1 the SI unit of \(a\) is coulomb
2 the SI unit of \(\lambda\) is per second
3 \(e^{\frac{t}{\lambda}}\) is unitless
4 the SI unit of \(a e^{\frac{t}{\lambda}}\) is ampere per second
Explanation:
\(I=a\left(1-e^{\frac{-t}{\lambda}}\right)\) Here, unit of \(I=\) unit of \(a=\) unit of \(a e^{\frac{-t}{\lambda}}\).
PHXI02:UNITS AND MEASUREMENTS
367338
Suppose refractive index \(\mu\) is given as \(\mu=A+B / \lambda^{2}\), where \(A\) and \(B\) are constants and \(\lambda\) is wavelength, then the dimension of \(B\) is same as that of
1 wavelength
2 pressure
3 area
4 volume
Explanation:
As, \(\mu=\dfrac{\text { Velocity of light in vaccum }}{\text { Velocity of light in medium }}\) The refractive index \(\mu\) is dimensionless, so each term on right hand side is dimensionless Hence, \(\dfrac{B}{\lambda^{2}}\) is also dimensionless. This implies that dimensions of \(B\) will have the dimensions of \(\lambda^{2}\), \(i.e\) of area.
PHXI02:UNITS AND MEASUREMENTS
367339
Which equation is dimensionally incorrect, where symbol represent their usual meaning?
367336
In the relation: \(\dfrac{d y}{d t}=2 \omega \sin \left(\omega t+\phi_{0}\right)\), the dimensional formula for \(\left(\omega t+\phi_{0}\right)\) is:
1 \([M L T]\)
2 \(\left[M L T^{0}\right]\)
3 \(\left[M L^{0} T^{0}\right]\)
4 \(\left[M^{0} L^{0} T^{0}\right]\)
Explanation:
Here, \(\left(\omega t+\phi_{0}\right)\) is dimensionless because it is an argument of a trigonometric function. Correct option is (4).
PHXI02:UNITS AND MEASUREMENTS
367337
If \(I=a\left(1-e^{\frac{t}{\lambda}}\right)\), then (where, \(I\) is electric current and \(t\) is time).
1 the SI unit of \(a\) is coulomb
2 the SI unit of \(\lambda\) is per second
3 \(e^{\frac{t}{\lambda}}\) is unitless
4 the SI unit of \(a e^{\frac{t}{\lambda}}\) is ampere per second
Explanation:
\(I=a\left(1-e^{\frac{-t}{\lambda}}\right)\) Here, unit of \(I=\) unit of \(a=\) unit of \(a e^{\frac{-t}{\lambda}}\).
PHXI02:UNITS AND MEASUREMENTS
367338
Suppose refractive index \(\mu\) is given as \(\mu=A+B / \lambda^{2}\), where \(A\) and \(B\) are constants and \(\lambda\) is wavelength, then the dimension of \(B\) is same as that of
1 wavelength
2 pressure
3 area
4 volume
Explanation:
As, \(\mu=\dfrac{\text { Velocity of light in vaccum }}{\text { Velocity of light in medium }}\) The refractive index \(\mu\) is dimensionless, so each term on right hand side is dimensionless Hence, \(\dfrac{B}{\lambda^{2}}\) is also dimensionless. This implies that dimensions of \(B\) will have the dimensions of \(\lambda^{2}\), \(i.e\) of area.
PHXI02:UNITS AND MEASUREMENTS
367339
Which equation is dimensionally incorrect, where symbol represent their usual meaning?
367336
In the relation: \(\dfrac{d y}{d t}=2 \omega \sin \left(\omega t+\phi_{0}\right)\), the dimensional formula for \(\left(\omega t+\phi_{0}\right)\) is:
1 \([M L T]\)
2 \(\left[M L T^{0}\right]\)
3 \(\left[M L^{0} T^{0}\right]\)
4 \(\left[M^{0} L^{0} T^{0}\right]\)
Explanation:
Here, \(\left(\omega t+\phi_{0}\right)\) is dimensionless because it is an argument of a trigonometric function. Correct option is (4).
PHXI02:UNITS AND MEASUREMENTS
367337
If \(I=a\left(1-e^{\frac{t}{\lambda}}\right)\), then (where, \(I\) is electric current and \(t\) is time).
1 the SI unit of \(a\) is coulomb
2 the SI unit of \(\lambda\) is per second
3 \(e^{\frac{t}{\lambda}}\) is unitless
4 the SI unit of \(a e^{\frac{t}{\lambda}}\) is ampere per second
Explanation:
\(I=a\left(1-e^{\frac{-t}{\lambda}}\right)\) Here, unit of \(I=\) unit of \(a=\) unit of \(a e^{\frac{-t}{\lambda}}\).
PHXI02:UNITS AND MEASUREMENTS
367338
Suppose refractive index \(\mu\) is given as \(\mu=A+B / \lambda^{2}\), where \(A\) and \(B\) are constants and \(\lambda\) is wavelength, then the dimension of \(B\) is same as that of
1 wavelength
2 pressure
3 area
4 volume
Explanation:
As, \(\mu=\dfrac{\text { Velocity of light in vaccum }}{\text { Velocity of light in medium }}\) The refractive index \(\mu\) is dimensionless, so each term on right hand side is dimensionless Hence, \(\dfrac{B}{\lambda^{2}}\) is also dimensionless. This implies that dimensions of \(B\) will have the dimensions of \(\lambda^{2}\), \(i.e\) of area.
PHXI02:UNITS AND MEASUREMENTS
367339
Which equation is dimensionally incorrect, where symbol represent their usual meaning?