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 \(\mathrm{v}=\mathrm{at}+\frac{\mathrm{b}}{\mathrm{t}+\mathrm{c}}\). The dimensions of \(\mathrm{a}\), \(\mathrm{b}\), and \(\mathrm{c}\) are respectively:
1. \( {\left[\mathrm{LT}^{-2}\right],[\mathrm{L}],[\mathrm{T}]} \)
2. \( {\left[\mathrm{L}^2\right],[\mathrm{T}] \text { and }\left[\mathrm{LT}^2\right]} \)
3. \( {\left[\mathrm{LT}^2\right],[\mathrm{LT}] \text { and }[\mathrm{L}]} \)
4. \( {[\mathrm{L}],[\mathrm{LT}], \text { and }\left[\mathrm{T}^2\right]}\)

Subtopic:  Dimensions |
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If the dimensions of a physical quantity are given by MaLbTc, 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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NEET - 2009
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The universal gravitational constant is dimensionally represented as:

1. ML2 T1

2. M2 L3 T2

3. M2 L2 T1

4. M1 L3 T2

Subtopic:  Dimensions |
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AIPMT - 2004
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Consider that 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
(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
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. \({\large\frac{\text{pressure}}{\text{acceleration}}},\text{ density}\)

 
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The dimensional formula of pressure is:

1. MLT-2

2. ML-1T2

3. ML-1T-2

4. MLT2

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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