The mass and volume of a body are \(4.237~\text{grams}\) and \(2.5~\text{cm}^3\), respectively. The density of the material of the body in correct significant figures will be:
1. \(1.6048~\text{grams cm}^{-3}\)
2. \(1.69~\text{grams cm}^{-3}\)
3. \(1.7~\text{grams cm}^{-3}\)
4. \(1.695~\text{grams cm}^{-3}\)
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. | \(164\pm3~\text{cm}^2\) | 2. | \(163.62\pm2.6~\text{cm}^2\) |
3. | \(163.6\pm2.6~\text{cm}^2\) | 4. | \(163.62\pm3~\text{cm}^2\) |
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) \(y = \left({\dfrac a T}\right) \sin \left({\dfrac t a}\right)\)
(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)
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 density of a material in a CGS system of units is \(4~\text{grams/cm}^3\). In a system of units in which the unit of length is \(10~\text{cm}\) and the unit of mass is \(100~\text{grams}\), the value of the density of the material will be:
1. \( 0.04 \)
2. \( 0.4 \)
3. \( 40 \)
4. \(400\)
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. \(2.14\%\)
An object is moving through a liquid. The viscous damping force acting on it is proportional to the velocity. Then the dimensions of the constant of proportionality are:
1. \(\left[ML^{-1}T^{-1}\right]\)
2. \(\left[MLT^{-1}\right]\)
3. \(\left[M^0LT^{-1}\right]\)
4. \(\left[ML^{0}T^{-1}\right]\)
The dimensions of \((\mu_0\varepsilon_0)^{\frac{-1}{2}}\) are:
1. \(\left[L^{-1}T\right]\)
2. \(\left[LT^{-1}\right]\)
3. \(\left[L^{{-1/2}}T^{{1/2}}\right]\)
4. \(\left[L^{{-1/2}}T^{{-1/2}}\right]\)