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 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 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 |
 84%
From NCERT
NEET - 2009
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Dimensions of electric current are:

1. [M0L0T1Q]

2. [ML2T1Q]

3. [M2LT1Q]

4. [M2L2T1Q]

Subtopic:  Dimensions |
 81%
From NCERT
PMT - 2000
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The position of a body with acceleration \(a\) is given by x=Kamt (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. MLT-2

2. ML-1T2

3. ML-1T-2

4. MLT2

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 |
 74%
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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