KCET · Physics · Units and Dimensions
Match the physical quantities given in List-I with dimensions expressed in terms of mass (M), length (L), time (T) and electric current (A) given in List-II.
| List-I | List-II |
|---|---|
| (a) Torque | (i) \([M^{-1}L^{-2}T^{4}A^{2}]\) |
| (b) Gravitational constant | (ii) \([M^{1}L^{2}T^{-1}]\) |
| (c) Capacitance | (iii) \([M^{-1}L^{3}T^{-2}]\) |
| (d) Planck's constant | (iv) \([M^{1}L^{2}T^{-2}]\) |
- A a - iv, b - ii, c - iii, d – i
- B a - iv, b - iii, c - i, d – ii
- C a - iv, b - i, c - iii, d – ii
- D a - ii, b - i, c - iii, d – iv
Answer & Solution
Correct Answer
(B) a - iv, b - iii, c - i, d – ii
Step-by-step Solution
Detailed explanation
Torque \(\tau = \text{Force} \times \text{Distance}\)
\([\tau] = [MLT^{-2}][L] = [M^{1}L^{2}T^{-2}]\)
Gravitational constant \(G = \dfrac{Fr^{2}}{m_{1}m_{2}}\)
\([G] = \dfrac{[MLT^{-2}][L^{2}]}{[M^{2}]} = [M^{-1}L^{3}T^{-2}]\)
Capacitance \(C = \dfrac{Q}{V} = \dfrac{Q^{2}}{W}\)
\([C] = \dfrac{[AT]^{2}}{[ML^{2}T^{-2}]} = [M^{-1}L^{-2}T^{4}A^{2}]\)
Planck's constant \(h = \dfrac{E}{\nu}\)
\([h] = \dfrac{[ML^{2}T^{-2}]}{[T^{-1}]} = [M^{1}L^{2}T^{-1}]\)
Thus, the correct matching is a - iv, b - iii, c - i, d - ii.
Answer: a - iv, b - iii, c - i, d – ii
\([\tau] = [MLT^{-2}][L] = [M^{1}L^{2}T^{-2}]\)
Gravitational constant \(G = \dfrac{Fr^{2}}{m_{1}m_{2}}\)
\([G] = \dfrac{[MLT^{-2}][L^{2}]}{[M^{2}]} = [M^{-1}L^{3}T^{-2}]\)
Capacitance \(C = \dfrac{Q}{V} = \dfrac{Q^{2}}{W}\)
\([C] = \dfrac{[AT]^{2}}{[ML^{2}T^{-2}]} = [M^{-1}L^{-2}T^{4}A^{2}]\)
Planck's constant \(h = \dfrac{E}{\nu}\)
\([h] = \dfrac{[ML^{2}T^{-2}]}{[T^{-1}]} = [M^{1}L^{2}T^{-1}]\)
Thus, the correct matching is a - iv, b - iii, c - i, d - ii.
Answer: a - iv, b - iii, c - i, d – ii
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