Q. No.| 1. | stress and energy |
| 2. | force and work |
| 3. | torque and work |
| 4. | velocity gradient and time |
If \(u_1\) and \(u_2\) are the units selected in two systems of measurement and \(n_1\) and \(n_2\) are their numerical values, then:
| 1. | \(n_1u_1=n_2u_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) |
| 2. | \(n_1u_1+n_2u_2=0\) |
| 3. | \(n_1n_2=u_1u_2\) |
| 4. | \((n_1+u_1)=(n_2+u_2)\) |
1. \(\left [\mathrm{ML}^{-1} \mathrm{~T}^{-2} \right] \)
2. \(\left [ \mathrm{ML}^{-2} \mathrm{~T}^{2} \right ] \)
3. \(\left [ \mathrm{MLT}^{-1} \right ] \)
4. \(\left [ \mathrm{ML}^{} \mathrm{~T}^{-2} \right ] \)
The velocity \(v\) of a particle at time \(t\) is given by \({v}={at}+\frac{{b}}{{t}+{c}}\). The dimensions of \({a}\), \({b}\), and \({c}\) are respectively:
1. \( {\left[{LT}^{-2}\right],[{L}],[{T}]} \)
2. \( {\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]} \)
3. \( {\left[{LT}^2\right],[{LT}] \text { and }[{L}]} \)
4. \( {[{L}],[{LT}], \text { and }\left[{T}^2\right]}\)
If the dimensions of a physical quantity are given by \(M^aL^bT^c\)
| 1. | pressure if \(a=1, ~b=-1,~c=-2\) |
| 2. | velocity if \(a=1,~b=0,~c=-1\) |
| 3. | acceleration if \(a=1,~b=1,~c=-2\) |
| 4. | force if \(a=0, ~b= -1,~c=-2\) |
| Column I | Column II | ||
| (A) | Dimensions of \(A\) | (P) | \([M^0L^0T^{-1}]\) |
| (B) | Dimensions of \(k_{1}\) | (Q) | \([M^0L^{-1}T^{-1}]\) |
| (C) | Dimensions of \(k_{2}\) | (R) | \([MLT^{-2}]\) |
| (D) | Dimensions of \(k_{1}k_{2}\) | (S) | \([M^0L^{-1}T^{0}]\) |
| 1. | A → R, B → S, C → P, D → Q |
| 2. | A → P, B → Q, C → R, D → S |
| 3. | A → R, B → P, C → Q, D → S |
| 4. | A → S, B → P, C → Q, D → R |
| 1. | \({\large\frac{\text{force}}{\text{volume}}},\text{ surface tension}\) |
| 2. | \(\text{torque},\text{ pressure}\times\text{volume}\) |
| 3. | \(\text{specific heat}\times\text{mass},\text{ energy}\) |
| 4. | \({\large\frac{\text{pressure}}{\text{acceleration}}},\text{ density}\) |
The dimensional formula of pressure is:
1. \(\left[MLT^{-2}\right]\)
2. \(\left[ML^{-1}T^{2}\right]\)
3. \(\left[ML^{-1}T^{-2}\right]\)
4. \(\left[MLT^{2}\right]\)
The dimensional formula for impulse is:
1. \([MLT^{-2}]\)
2. \([MLT^{-1}]\)
3. \([ML^2T^{-1}]\)
4. \([M^2LT^{-1}]\)
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