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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Given the equation \(\left(P+\frac{a}{V^2}\right)(V-b)=\text {constant}\). The units of \(a\) will be: (where \(P\) is pressure and \(V\) is volume)
1. \(\text{dyne} \times \text{cm}^5\)
2. \(\text{dyne} \times \text{cm}^4\)
3. \(\text{dyne} / \text{cm}^3\)
4. \(\text{dyne} / \text{cm}^2\)

Subtopic:  Dimensions |
 60%
From NCERT
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The dimensions of a couple are:
1. \(\left[ML^2T^{-2}\right]\)
2. \(\left[MLT^{-2}\right]\)
3. \(\left[ML^{-1}T^{-3}\right]\)
4. \(\left[ML^{-2}T^{-2}\right]\)

Subtopic:  Dimensions |
 63%
From NCERT
PMT - 1972
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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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The dimensions of resistivity in terms of \(M\), \(L\), \(T\), and \(Q\) where \(Q\) stands for the dimensions of charge, will be:
1. \(\left[M L^3 T^{-1} Q^{-2}\right]\)
2. \(\left[M L^3 T^{-2} Q^{-1}\right]\)
3. \(\left[M L^2 T^{-1} Q^{-1}\right]\)
4. \(\left[M L T^{-1} Q^{-1}\right]\)

Subtopic:  Dimensions |
 63%
From NCERT
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Dimensions of electric current are:
1. \(\left[M^0L^0T^{-1}Q\right]\)
2. \(\left[M^1L^2T^{-1}Q\right]\)
3. \(\left[M^2L^1T^{-1}Q\right]\)
4. \(\left[M^2L^2T^{-1}Q\right]\)

Subtopic:  Dimensions |
 82%
From NCERT
PMT - 2000
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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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The position of a body with acceleration \(a\) is given by \(x= Ka^{m}t^{n}\) (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 period of oscillation of a simple pendulum is given by T=2πlg where l is about 100 cm and is known to have 1 mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stopwatch of least count 0.1 s. The percentage error in g is:

1. 0.1%

2. 1%

3. 0.2%

4. 0.8%

Subtopic:  Errors |
 50%
From NCERT
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The percentage errors in the measurement of mass and speed are \(2\%\) and \(3\%\) respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed:
1. \(11\%\)
2. \(8\%\)
3. \(5\%\)
4. \(1\%\)

Subtopic:  Errors |
 85%
From NCERT
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