Q. No.The main scale of a vernier calliper has \(n\) divisions/cm. \(n\) divisions of the vernier scale coincide with \((n-1)\) divisions of the main scale. The least count of the vernier calliper is:
1. \(\dfrac{1}{(n+1)(n-1)}\) cm
2. \(\dfrac{1}{n}\) cm
3. \(\dfrac{1}{n^{2}}\) cm
4. \(\dfrac{1}{(n)(n+1)}\) cm
1. \(\dfrac{1}{(n+1)(n-1)}\) cm
2. \(\dfrac{1}{n}\) cm
3. \(\dfrac{1}{n^{2}}\) cm
4. \(\dfrac{1}{(n)(n+1)}\) cm
Which of the following expressions have units of power?
| (A) | \(\dfrac{mv^2}{2t}\) |
| (B) | \(\dfrac{V^2}{R}\) |
| (C) | \(\dfrac{mgh}{t}\) |
| 1. | (A) and (B) only |
| 2. | (A) only |
| 3. | (B) and (C) only |
| 4. | (A), (B), and (C) |
Four students measure the height of a tower. Each student uses a different method and each measures the height many times. The data for each are plotted below. The measurement with the highest precision is:
| (I) |  |
(II) |  |
| (III) |  |
(IV) |  |
1. I
2. II
3. III
4. IV
Given below are two statements:
| Assertion (A): | A dimensionally incorrect equation cannot ever be correct. |
| Reason (R): | Physically correct equations must be dimensionally correct. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
If \({x}=\dfrac{{a} \sin \theta+{b} \cos \theta}{{a}+{b}},\) then:
| 1. | the dimensions of \(x\) and \(a\) must be the same |
| 2. | the dimensions of \(a\) and \(b\) are not the same |
| 3. | \(x\) is dimensionless |
| 4. | none of the above |
In an experiment, the percentage errors that occurred in the measurement of physical quantities \(A,\) \(B,\) \(C,\) and \(D\) are \(1\%\), \(2\%\), \(3\%\), and \(4\%\) respectively. Then, the maximum percentage of error in the measurement of \(X,\) where \(X=\frac{A^2 B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^3}\), will be:
1. \(10\%\)
2. \(\frac{3}{13}\%\)
3. \(16\%\)
4. \(-10\%\)
\(P=\dfrac{a^3b^2}{cd}\)
Percentage error in \(P\) is:
1. \(10\%\)
2. \(7\%\)
3. \(4\%\)
4. \(14\%\)
If force (\(F\)), velocity (\(\mathrm{v}\)), and time (\(T\)) are taken as fundamental units, the dimensions of mass will be:
| 1. | \([FvT^{-1}]\) | 2. | \([FvT^{-2}]\) |
| 3. | \([Fv^{-1}T^{-1}]\) | 4. | \([Fv^{-1}T]\) |
1. \([Ev^{-2}T^{-1}]\)
2. \([Ev^{-1}T^{-2}]\)
3. \([Ev^{-2}T^{-2}]\)
4. \([E^{-2}v^{-1}T^{-3}]\)
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