Q. No.The mass and volume of a body are \(4.237~\mathrm{g}\) and \(2.5~\mathrm{cm^3}\), respectively. The density of the material of the body in correct significant figures will be:
1. \(1.6048~\mathrm{g~cm^{-3}}\)
2. \(1.69~\mathrm{g~cm^{-3}}\)
3. \(1.7~\mathrm{g~cm^{-3}}\)
4. \(1.695~\mathrm{g~cm^{-3}}\)
1. \(1.6048~\mathrm{g~cm^{-3}}\)
2. \(1.69~\mathrm{g~cm^{-3}}\)
3. \(1.7~\mathrm{g~cm^{-3}}\)
4. \(1.695~\mathrm{g~cm^{-3}}\)
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 \(2.74\) |
Young's modulus of steel is \(1.9 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\). When expressed in CGS units of \(\mathrm{dyne/cm^2}\), it will be equal to: \((1 \mathrm{~N}=10^5 \text { dyne, } 1 \mathrm{~m}^2=10^4 \mathrm{~cm}^2)\)
1. \( 1.9 \times 10^{10} \)
2. \( 1.9 \times 10^{11} \)
3. \( 1.9 \times 10^{12} \)
4. \( 1.9 \times 10^9\)
1. \( {\left[\mathrm{pA}^{-1} \mathrm{~T}^1\right]} \)
2. \( {\left[\mathrm{p}^2 \mathrm{AT}\right]} \)
3. \( {\left[\mathrm{pA}^{-1 / 2} \mathrm{~T}\right]} \)
4. \( {\left[\mathrm{pA}^{1 / 2} \mathrm{~T}^{-1}\right]}\)
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. \(y = \left({a \over T}\right) \sin \left({t \over a}\right)\)
d. \(y = a \sqrt 2 \left(\sin \left({2 \pi t \over T}\right) - \cos \left({2 \pi t \over T}\right)\right)\)
(Symbols have their usual meanings.)
Choose the correct option:
1. (a), (c)
2. (a), (b)
3. (b), (c)
4. (a), (d)
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 angle of \(1'\) (minute of an arc) in radian is nearly equal to:
1. \(2.91 \times 10^{-4} ~\mathrm{rad} \)
2. \(4.85 \times 10^{-4} ~\mathrm{rad} \)
3. \(4.80 \times 10^{-6} ~\mathrm{rad} \)
4. \(1.75 \times 10^{-2} ~\mathrm{rad}\)
The angle of \(1^\circ\) (degree) will be equal to:
(Use \(360^\circ=2\pi\) rad)
1. \(1.034\times10^{-3}\) rad
2. \(1.745\times10^{-2}\) rad
3. \(1.524\times10^{-2}\) rad
4. \(1.745\times10^{3}\) rad
Each side of a cube is measured to be \(7.203\) \(\mathrm{m}.\) What are the total surface area and the volume respectively of the cube to appropriate significant figures?
| 1. | \(373.7~\mathrm{m^2}\) and \(311.3~\mathrm{m^3}\) |
| 2. | \(311.3~\mathrm{m^2}\) and \(373.7~\mathrm{m^3}\) |
| 3. | \(311.2992~\mathrm{m^2}\) and \(373.7147~\mathrm{m^3}\) |
| 4. | \(373.7147~\mathrm{m^2}\) and \(311.2992~\mathrm{m^3}\) |
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 |
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