In an experiment, the height of an object measured by a vernier callipers having least count of \(0.01~\mathrm{cm}\) is found to be \(5.72~\mathrm{cm}\). When no object is there between jaws of this vernier callipers, the reading of the main scale is \(0.1\) cm and the reading of the vernier scale is \(0.3~\mathrm{mm}\). The correct height of the object is:
1. \( 5.72 \mathrm{~cm} \)
2. \( 5.59 \mathrm{~cm} \)
3. \( 5.85 \mathrm{~cm} \)
4. \( 5.69 \mathrm{~cm}\)
A thin wire has a length of \(21.7~\mathrm{cm}\) and a radius of \(0.46~\mathrm{mm}\). The volume of the wire to correct significant figures is:
1. | \( 0.15 \mathrm{~cm}^3 \) | 2. | \( 0.1443 \mathrm{~cm}^3 \) |
3. | \( 0.14 \mathrm{~cm}^3 \) | 4. | \( 0.144 \mathrm{~cm}^3\) |
If \({x}=\frac{{a} \sin \theta+{b} \cos \theta}{{a}+{b}}\),
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 screw gauge has the least count of \(0.01~\mathrm{mm}\) and there are \(50\) divisions in its circular scale. The pitch of the screw gauge is:
1. \(0.25\) mm
2. \(0.5\) mm
3. \(1.0\) mm
4. \(0.01\) mm
Taking into account the significant figures, what is the value of \((9.99~\mathrm{m}-0.0099~\mathrm{m})\)?
1. | \(9.98\) m | 2. | \(9.980\) m |
3. | \(9.9\) m | 4. | \(9.9801\) m |
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. \(0.0\pm0.4\)
In which of the following, the number of significant figures is different from that in the others?
1. \(2.303~\mathrm{kg}\)
2. \(12.23~\mathrm{m}\)
3. \(0.002\times10^{5}~\mathrm{m}\)
4. \(2.001\times10^{-3}~\mathrm{kg}\)
Which of the following relations is dimensionally wrong? [The symbols have their usual meanings]
1. \(s= ut+\frac{1}{6}at^2\)
2. \(v^2= u^2+\frac{2as^2}{\pi}\)
3. \(v= u-2at\)
4. All of these
When units of mass, length, and time are taken as \(10~\text{kg}, 60~\text{m}~\text{and}~60~\text{s}\) 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. \(120\)
If \(\int \frac{d x}{\sqrt{a^2-x^2}}=a^n \sin ^{-1} \frac{x}{a}\) is dimensionally correct, then the value of \(n\) will be:
1. \(1\)
2. \(\text{zero}\)
3. \(\text-1\)
4. \(2\)