The thickness of a pencil measured by using a screw gauge (least count \(0.001\) cm) comes out to be \(0.802\) cm. The percentage error in the measurement is:
1. \(0.125 \%\)
2. \(2.43\%\)
3. \(4.12\%\)
4. \(2.14\%\)
Which of the following measurements is the most precise?
1. 5.00 mm
2. 5.00 cm
3. 5.00 m
4. 5.00 km
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 \(4.237~\mathrm{g}\) 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. \(1.695~\mathrm{g~cm^{-3}}\)
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 \(2.74\) |
The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error would be, respectively,
1. 164 3
2. 163.62 2.6
3. 163.6 2.6
4. 163.62 3
The mean length of an object is \(5~\text{cm}\). Which of the following measurements is the most accurate?
1. \(4.9~\text{cm}\)
2. \(4.805~\text{cm}\)
3. \(5.25~\text{cm}\)
4. \(5.4~\text{cm}\)
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)
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. \(0.0\pm0.4\)
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 |