Select Chapter Topics:
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 ${\mathrm{}}^{}$$$[M^aL^bT^c],$$ 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 |
85%
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 |
86%
From NCERT
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 |
79%
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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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From NCERT
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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 |
79%
From NCERT
PMT - 1991
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