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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)$$
Subtopic:  Dimensions |
85%
From NCERT
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The dimensional formula of modulus of rigidity is:
1. $$\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 ]$$
Subtopic:  Dimensions |
79%
From NCERT
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The velocity v of a particle at time $$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 |
85%
From NCERT
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If the dimensions of a physical quantity are given by ${\mathrm{M}}^{\mathrm{a}}{\mathrm{L}}^{\mathrm{b}}{\mathrm{T}}^{\mathrm{c}},$ 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 |
84%
From NCERT
NEET - 2009
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The universal gravitational constant is dimensionally represented as:

1.

2.

3.

4.

Subtopic:  Dimensions |
85%
From NCERT
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 |
80%
From NCERT
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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 |
78%
From NCERT
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The dimensional formula of pressure is:

1. $\left[{\mathrm{MLT}}^{-2}\right]$

2. $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{2}\right]$

3. $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]$

4. $\left[{\mathrm{MLT}}^{2}\right]$

Subtopic:  Dimensions |
80%
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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