If L denotes the inductance of an inductor through which a current i is flowing, the dimensions of Li2 are
1. ML2T−2ML2T−2
2. Not expressible in MLT
3. MLT−2MLT−2
4. LT
Of the following quantities, which one has dimensions different from the remaining three
1. Energy per unit volume
2. Force per unit area
3. Product of voltage and charge per unit volume
4. Angular momentum per unit mass
A spherical body of mass m and radius r is allowed to fall in a medium of viscosity ηη. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v)(v) is called time constant (τ)(τ). Dimensionally ττ can be represented by
1. mr26πηmr26πη
2. √(6πmrηg2)√(6πmrηg2)
3. m6πηrvm6πηrv
4. None of the above
The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f=C mxKyf=C mxKy; where C is a dimensionless quantity. The value of x and y are
1. x=12, y=12x=12, y=12
2. x=−12,y=−12x=−12,y=−12
3. x=12,y=−12x=12,y=−12
4. x=−12,y=12
The quantities A and B are related by the relation, m = A/B, where m is the linear density and A is the force. The dimensions of B are of
1. Pressure
2. Work
3. Latent heat
4. None of the above
The velocity of water waves v may depend upon their wavelength λ, the density of water ρ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as:
1. v2∝gλ-1ρ-1
2. v2∝gλρ
3. v2∝gλ
4. v2∝g−1λ−3
The dimensions of resistivity in terms of M, L, T, and Q where Q stands for the dimensions of charge, will be:
1. [ML3T−1Q−2]
2. [ML3T−2Q−1]
3. [ML2T−1Q−1]
4. [MLT−1Q−1]
The dimensions of Farad are , where Q represents electric charge [This question includes concepts from 12th syllabus]
1. M−1L−2T2Q2
2. M−1L−2TQ
3. M−1L−2T−2Q
4. M−1L−2TQ2
The equation of a wave is given by Y=Asinω(xv−k) where ω is the angular velocity, x is length and v is the linear velocity. The dimension of k is
1. LT
2. T
3. T−1
4. T2
Dimensional formula of capacitance is
1. M−1L−2T4A2
2. ML2T4A−2
3. MLT−4A2
4. M−1L−2T−4A−2