Q. No.| 1. | stress and energy |
| 2. | force and work |
| 3. | torque and work |
| 4. | velocity gradient and time |
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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. | \((n_1+u_1)=(n_2+u_2)\) |
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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. \(\left [ \mathrm{ML}^{} \mathrm{~T}^{-2} \right ] \)
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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. \( {[{L}],[{LT}], \text { and }\left[{T}^2\right]}\)
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| 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 \(a=0, ~b= -1,~c=-2\) |
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The universal gravitational constant is dimensionally represented as:
1. \(\left[ML^2T^{-1}\right]\)
2. \(\left[M^{-2}L^3T^{-2}\right]\)
3. \(\left[M^{-2}L^2T^{-1}\right]\)
4. \(\left[M^{-1}L^3T^{-2}\right]\)
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| Column I | Column II | ||
| \((\mathrm A)\) | Dimensions of \(A\) | \((\mathrm P)\) | \([M^0L^0T^{-1}]\) |
| \((\mathrm B)\) | Dimensions of \(k_{1}\) | \((\mathrm Q)\) | \([M^0L^{-1}T^{-1}]\) |
| \((\mathrm C)\) | Dimensions of \(k_{2}\) | \((\mathrm R)\) | \([MLT^{-2}]\) |
| \((\mathrm D)\) | Dimensions of \(k_{1}k_{2}\) | \((\mathrm S)\) | \([M^0L^{-1}T^{0}]\) |
| 1. | \(\mathrm {A \rightarrow R, B \rightarrow S, C \rightarrow P, D \rightarrow Q }\) |
| 2. | \(\mathrm {A \rightarrow P, B \rightarrow Q, C \rightarrow R, D \rightarrow S }\) |
| 3. | \(\mathrm {A \rightarrow R, B \rightarrow P, C \rightarrow Q, D \rightarrow S }\) |
| 4. | \(\mathrm {A \rightarrow S, B \rightarrow P, C \rightarrow Q, D \rightarrow R}\) |
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| 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. | \({\large\frac{\text{pressure}}{\text{acceleration}}},\text{ density}\) |
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| 1. | \(\left[MLT^{-2}\right]\) | 2. | \(\left[ML^{-1}T^{2}\right]\) |
| 3. | \(\left[ML^{-1}T^{-2}\right]\) | 4. | \(\left[MLT^{2}\right]\) |
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| 1. | \([MLT^{-2}]\) | 2. | \([MLT^{-1}]\) |
| 3. | \([ML^2T^{-1}]\) | 4. | \([M^2LT^{-1}]\) |
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