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  • A physical quantity Q depends on the variables  as <img alt="Q = kx^2 y^3/z^2,"

A physical quantity Q depends on the variables x, y \ and \ z as Q = kx^2 y^3/z^2, where  k is a constant of proportionality. If the dimensions of x, y \ and \ z are L, M and T, respectively, then the dimensions of k in terms of L, M and T are:

Option: 1

L^{-2} M^{-3} T^2


Option: 2

L^2 M^3 T^{-2}


Option: 3

L^{-1} M^{-1} T^{-1}


Option: 4

L^2 M^{-3} T^2


Answers (1)

best_answer

 The given equation can be written as:

Q = k \cdot x^2 \cdot y^3 \cdot z^{-2}

Therefore, the dimensions of Q are:

L^2 \cdot M^3 \cdot T^{-2}

Equating the dimensions on both sides, we get: 

[k] = [Q] \cdot [x]^{-2} \cdot [y]^{-3} \cdot [z]^{2}

[k] = L^2 \cdot M^3 \cdot T^{-2} \cdot L^{-2} \cdot M^{-3} \cdot T^{2}

[k] = L^2 \cdot M^{-3} \cdot T^{2}

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Sayak

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