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Dimensions of constants in an expression whose added terms must have the same dimension

This type of question, asked 6 times: 2021 Paper 15, 31 Jan 2024, 23 Jan 2025, 29 Jan 2025, 21 Jan 2026 S1, 6 Apr 2026 S1. All 8 questions below, oldest first.

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  1. Question 1

    2021 Paper 15

    2
    For the force equation F=Acos(Bx)+Csin(Dt)F=Acos(Bx) +Csin(Dt). Find dimensions of ADB\frac{AD}{B} ?

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  2. Question 2

    31 Jan 2024

    110
    Consider two physical quantities AA and BB related to each other as E=B−x2AtE =\frac{B -x^{2}}{At} where E,xE,x and tt have dimensions of energy, length and time respectively. The dimension of ABAB is

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  3. Question 3

    31 Jan 2024

    11
    A force is represented by F=ax2+bt1/2F =ax^{2}+bt^{1/2} Where x=x = distance and t=t = time. The dimensions of b2/ab^{2}/a are :

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  4. Question 4

    23 Jan 2025

    16
    The electric flux is ϕ=ασ+βλ\phi = \alpha\sigma + \beta\lambda where λ\lambda and σ\sigma are linear and surface charge density, respectively, (αβ)\left( \frac{\alpha}{\beta} \right) represents

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  5. Question 5

    23 Jan 2025

    8
    The position of a particle moving on xx-axis is given by x(t)=Asin⁡t+Bcos⁡2t+Ct2+Dx(t) = A\sin t + B\cos^{2}t + Ct^{2}+ D, where tt is time. The dimension of ABCD\frac{ABC}{D} is-

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  6. Question 6

    29 Jan 2025

    6
    The expression given below shows the variation of velocity (v) with time ( t ), v=At2+BtC+tv =At^{2}+\frac{Bt}{C + t}. The dimension of ABC is :

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  7. Question 7

    21 Jan 2026 S1

    7
    Consider a modified Bernoulli equation.
    (P+ABt2)+ρg( h+Bt)+12ρ V2= constant \left( P +\frac{A}{Bt^{2}} \right)+ \rho g(\text{ }h + Bt) +\frac{1}{2}\rho{\text{ }V}^{2}=\text{~constant~}
    If t has the dimension of time then the dimensions of A and B are ____\_\_\_\_ , ____\_\_\_\_ respectively.

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  8. Question 8

    6 Apr 2026 S1

    2
    The potential energy of a particle changes with distance xx from a fixed origin as V=Axx+BV=\frac{A\sqrt{x}}{x+B}, where A and B are constant with appropriate dimensions. The dimension of AB are ____\_\_\_\_ .

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