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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)$$
Subtopic:  Dimensions |
85%
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The velocity v of a particle at time $$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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Dimensions of electric current are:

1. $\left[{M}^{0}{L}^{0}{T}^{-1}Q\right]$

2. $\left[M{L}^{2}{T}^{-1}Q\right]$

3. $\left[{M}^{2}L{T}^{-1}Q\right]$

4. $\left[{M}^{2}{L}^{2}{T}^{-1}Q\right]$

Subtopic:  Dimensions |
81%
From NCERT
PMT - 2000
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The position of a body with acceleration $$a$$ is given by  (assume $$t$$ to be time). The values of m and n will be:

1. m = 1, n = 1

2. m = 1, n = 2

3. m = 2, n = 1

4. m = 2, n = 2

Subtopic:  Dimensions |
77%
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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In the relation, $$y=a \cos (\omega t-k x)$$, the dimensional formula for $$k$$ will be:
1. $${\left[M^0 L^{-1} T^{-1}\right]}$$
2. $${\left[M^0 L T^{-1}\right]}$$
3. $${\left[M^0 L^{-1} T^0\right]}$$
4. $${\left[M^0 L T\right]}$$

Subtopic:  Dimensions |
78%
From NCERT
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When units of mass, length, and time are taken as 10 kg, 60 m, and 60 s respectively, the new unit of energy becomes $$x$$ times the initial SI unit of energy. The value of $$x$$ will be:
1. 10
2. 20
3. 60
4. 120

Subtopic:  Dimensions |
75%
From NCERT
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If the units of force and length, each is increased by four times, then the unit of energy increases by:

 1 16 times 2 8 times 3 2 times 4 4 times
Subtopic:  Dimensions |
77%
From NCERT
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