If u1 and u2 are the units selected in two systems of measurement and n1 and n2 are their numerical values, then

1. ${n}_{1}{u}_{1}={n}_{2}{u}_{2}$

2. ${n}_{1}{u}_{1}+{n}_{2}{u}_{2}=0$

3. ${n}_{1}{n}_{2}={u}_{1}{u}_{2}$

4. $\left({n}_{1}+{u}_{1}\right)=\left({n}_{2}+{u}_{2}\right)$

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 a, b and c are respectively:

1.

2.

3.

4.

Subtopic:  Dimensions |
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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 |
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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 |
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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 |
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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 |
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The dimensional formula for impulse is

1. $ML{T}^{-2}$

2. $ML{T}^{-1}$

3. $M{L}^{2}{T}^{-1}$

4. ${M}^{2}L{T}^{-1}$

Subtopic:  Dimensions |
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In the relation $y=a\mathrm{cos}\left(\omega t-kx\right)$, 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. $\left[{M}^{0}LT\right]$

Subtopic:  Dimensions |
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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 |
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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 |
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