Identify the pair whose dimensions are equal:
1. stress and energy
2. force and work
3. torque and work
4. velocity gradient and time
Subtopic:  Dimensions |
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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. \((n_1+u_1)=(n_2+u_2)\)
Subtopic:  Dimensions |
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The dimensional formula of modulus of rigidity is:
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. \(\left [ \mathrm{ML}^{} \mathrm{~T}^{-2} \right ] \)
Subtopic:  Dimensions |
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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. \( {[{L}],[{LT}], \text { and }\left[{T}^2\right]}\)

Subtopic:  Dimensions |
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If the dimensions of a physical quantity are given by \([M^aL^bT^c],\) then the physical quantity will be:

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 \(a=0, ~b= -1,~c=-2\)
Subtopic:  Dimensions |
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From NCERT
NEET - 2009
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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. \(\left[M^{-1}L^3T^{-2}\right]\)

Subtopic:  Dimensions |
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AIPMT - 2004
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The force \(F\) acting on a body as a function of position \((x)\) and time \((t)\) is expressed as \(F=A \sin \left(k_1 x\right)+B \cos \left(k_2 t\right).\) From the given information, match Column I with Column II.
 
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 \(k_{1}k_{2}\) \((\mathrm S)\) \([M^0L^{-1}T^{0}]\)
Codes:
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. \(\mathrm {A \rightarrow S, B \rightarrow P, C \rightarrow Q, D \rightarrow R}\)
Subtopic:  Dimensions |
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Which, among the pairs of quantities has the same dimensions?
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. \({\large\frac{\text{pressure}}{\text{acceleration}}},\text{ density}\)
Subtopic:  Dimensions |
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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. \(\left[MLT^{2}\right]\)

Subtopic:  Dimensions |
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The dimensional formula for impulse is:
1. \([MLT^{-2}]\)
2. \([MLT^{-1}]\)
3. \([ML^2T^{-1}]\)
4. \([M^2LT^{-1}]\)

Subtopic:  Dimensions |
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PMT - 1991
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