Q. No.The number of significant figures in \(0.0006032~\text m^2\) is:
1.
\(4 \)
2.
\(5\)
3.
\(7\)
4.
\(3\)
If \(x=10.0\pm0.1\) and \(y=10\pm0.1\), then \(2x-2y\) with consideration of significant figures is equal to:
1. zero
2. \(0.0\pm0.1\)
3. \(0.0\pm0.2\)
4. \(0.0\pm0.4\)
| 1. | \(9.98~\text{m}\) | 2. | \(9.980~\text{m}\) |
| 3. | \(9.9~\text{m}\) | 4. | \(9.9801~\text{m}\) |
A screw gauge has the least count of \(0.01~\text{mm}\) and there are \(50\) divisions in its circular scale. The pitch of the screw gauge is:
| 1. | \(0.25~\text{mm}\) | 2. | \(0.5~\text{mm}\) |
| 3. | \(1.0~\text{mm}\) | 4. | \(0.01~\text{mm}\) |
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 |
A thin wire has a length of \(21.7~\text{cm}\) and a radius of \(0.46~\text{mm}\). The volume of the wire to correct significant figures is:
| 1. | \( 0.15~ \text{cm}^3 \) | 2. | \( 0.1443~ \text{cm}^3 \) |
| 3. | \( 0.14~ \text{cm}^3 \) | 4. | \( 0.144 ~\text{cm}^3\) |
The sum of the numbers \(436.32,227.2,\) and \(0.301\) in the appropriate significant figures is:
| 1. | \( 663.821 \) | 2. | \( 664 \) |
| 3. | \( 663.8 \) | 4. | \(663.82\) |
The mass and volume of a body are \(4.237~\text{g }\) and \(2.5~\text{cm}^3,\) respectively. The density of the material of the body in correct significant figures will be:
1. \(1.6048~\text{g cm}^{-3}\)
2. \(1.69~\text{g cm}^{-3}\)
3. \(1.7~\text{g cm}^{-3}\)
4. \(1.695~\text{g cm}^{-3}\)
The numbers \(2.745\) and \(2.735\) on rounding off to \(3\) significant figures will give respectively,
| 1. | \(2.75\) and \(2.74\) | 2. | \(2.74\) and \(2.73\) |
| 3. | \(2.75\) and \(2.73\) | 4. | \(2.74\) and \(2.74\) |
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is/are not correct.
| (a) | \(y = a\sin \left(2\pi t / T\right)\) |
| (b) | \(y = a\sin(vt)\) |
| (c) | \(y = \left({\dfrac a T}\right) \sin \left({\dfrac t a}\right)\) |
| (d) | \(y = a \sqrt 2 \left(\sin \left({\dfrac {2 \pi t} T}\right) - \cos \left({\dfrac {2 \pi t} T}\right)\right)\) |
(Symbols have their usual meanings.)
Choose the correct option:
| 1. | (a), (c) |
| 2. | (a), (b) |
| 3. | (b), (c) |
| 4. | (a), (d) |
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