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Find the exponents in a formula by dimensional analysis

This type of question, asked 4 times: 24 Jan 2023, 15 Apr 2023, 23 Jan 2026 S2, 8 Apr 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    24 Jan 2023

    92
    The frequency (v)(v) of an oscillating liquid drop may depend upon radius (r)(r) of the drop, density (ρ)(\rho) of liquid and the surface tension (s) of the liquid as: v=raρbscv =r^{a}\rho^{b}s^{c}. The values of a,ba,b and cc respectively are

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  2. Question 2

    15 Apr 2023

    17
    The speed of a wave produced in water is given by v=λagbρcv =\lambda^{a}g^{b}\rho^{c}. Where λ,g\lambda,g and ρ\rho are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a,ba,b and cc respectively, are:

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  3. Question 3

    23 Jan 2026 S2

    23
    A ball of radius r and density ρ\rho dropped through a viscous liquid of density σ\sigma and viscosity η\eta attains its terminal velocity at time t , given by t=Aρarbηcσdt = A\rho^{a}r^{b}\eta^{c}\sigma^{d}, where A is a constant and a,b,ca, b, c and dd are integers. The value of b+ca+d\frac{b + c}{a + d} is ____\_\_\_\_ .

  4. Question 4

    8 Apr 2026 S2

    2
    Consider the equation H=xp∈qErtsH=\frac{x^{p}\in^{q}E^{r}}{t^{s}} Where H=H = magnetic field; E=E = electric field; ϵ=\epsilon= permittivity, x=x = distance, t=t = time. The values of p,q,rp,q,r and ss respectively are :

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