A spherical body of mass m and radius r is allowed to fall in a medium of viscosity η. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant (τ). Dimensionally τ can be represented by
1. mr26πη
2. √(6πmrηg2)
3. m6πηrv
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 mxKy; where C is a dimensionless quantity. The value of x and y are
1. x=12, y=12
2. x=−12,y=−12
3. x=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
Dimensional formula of heat energy is
1. ML2T−2
2. MLT−1
3. M0L0T−2
4. None of these
If C and L denote capacitance and inductance respectively, then the dimensions of LC are
1. M0L0T0
2. M0L0T2
3. M2L0T2
4. MLT2