Four students measure the height of a tower. Each student uses a different method and each measures the height many times. The data for each are plotted below. The measurement with the highest precision is:
(I) | ![]() |
(II) | ![]() |
(III) | ![]() |
(IV) | ![]() |
1. I
2. II
3. III
4. IV
Which of the following equations is dimensionally correct?
\((I)~~ v=\sqrt{\dfrac{P}{\rho}}~~~~~~(II)~~v=\sqrt{\dfrac{mgl}{I}}~~~~~~(III)~~v=\dfrac{Pr^2}{2\eta l}\)
(where \(v=\) speed, \(P=\) pressure; \(r,\) \(l\) are lengths; \(\rho=\) density, \(m=\) mass, \(g=\) acceleration due to gravity, \(I=\) moment of inertia, and \(\eta=\) coefficient of viscosity)
1. | \(I~ \text{and}~II\) |
2. | \(I~ \text{and}~III\) |
3. | \(II~ \text{and}~III\) |
4. | \(I,~II~\text{and}~III\) |
List-I | List-II | ||
(a) | H/s | (i) | s2 |
(b) | H×A | (ii) | Wb |
(c) | H×F | (iii) | s |
(d) | \(\Omega\)×F | (iv) | \(\Omega\) |
1. | (a)–(ii), (b)–(iv), (c)–(i), (d)–(iii) |
2. | (a)–(iv), (b)–(ii), (c)–(i), (d)–(iii) |
3. | (a)–(iv), (b)–(ii), (c)–(iii), (d)–(i) |
4. | (a)–(ii), (b)–(iii), (c)–(iv), (d)–(i) |
List-I | List-II | ||
(a) | acceleration | (i) | \([M^0L^0T^0 ]\) |
(b) | torque | (ii) | \([ML^{-1}T^{-2} ]\) |
(c) | absorptive power | (iii) | \([LT^{-2} ]\) |
(d) | pressure | (iv) | \([ML^2T^{-2} ]\) |
1. | (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) |
2. | (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv) |
3. | (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv) |
4. | (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i) |
List-I | List-II | ||
(a) | Ohm | (i) | \([ML^2T^{-2}A^{-1}]\) |
(b) | Farad | (ii) | \([ML^2T^{-2}A^{-2}]\) |
(c) | Henry | (iii) | \([M^{-1}L^{-2}T^4A^2]\) |
(d) | Weber | (iv) | \([ML^2T^{-3}A^{-2}]\) |
1. | (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) |
2. | (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii) |
3. | (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv) |
4. | (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) |
Which two of the following five physical parameters have the same dimensions?
(1) | Energy density |
(2) | Refractive index |
(3) | Dielectric constant |
(4) | Young's modulus |
(5) | Magnetic field |
Choose the correct option:
1. | (2) and (4) |
2. | (3) and (5) |
3. | (1) and (4) |
4. | (1) and (5) |
Match List-I with List-II:
List-I | List-II | ||
(a) | \(h\) (Planck's constant) | (i) | \(\left[ MLT^{-1} \right]\) |
(b) | \(E\) (kinetic energy) | (ii) | \(\left[ ML^{2}T^{-1} \right]\) |
(c) | \(V\) (electric potential) | (iii) | \(\left[ ML^{2}T^{-2} \right]\) |
(d) | \(p\) (linear momentum) | (iv) | \(\left[ ML^{2}A^{-1}T^{-3} \right]\) |
1. | (a) → (iii), (b) → (iv), (c) → (ii), (d) → (i) |
2. | (a) → (ii), (b) → (iii), (c) → (iv), (d) → (i) |
3. | (a) → (i), (b) → (ii), (c) → (iv), (d) → (iii) |
4. | (a) → (iii), (b) → (ii), (c) → (iv), (d) → (i) |
(A) | \(\dfrac{\text{(Magnetic flux)}^2}{\text{Electrical resistance}}\) | (B) | \(\text{Torque}\times\text{time}\) |
(C) | \(\text{Momentum}\times\text{length}\) | (D) | \(\dfrac{\text{Power}}{\text{time}}\) |
(A) | \(\dfrac{\text{electric field }\times\text{ magnetic field}}{\mu_0}\) |
(B) | \(\dfrac{\varepsilon_0\times\text{(electric potential)}^2\times\text{ velocity}}{\text{area}}\) |
(C) | \(\dfrac{\text{power}}{\text{area}}\) |