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. \(y = \left({a \over T}\right) \sin \left({t \over a}\right)\)
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 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 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 \(4~\text{g/cm}^3\). In a system of units in which the unit of length is \(10~\text{cm}\) and the unit of mass is \(100~\text{g}\), the value of the density of the material will be:
1. \( 0.04 \)
2. \( 0.4 \)
3. \( 40 \)
4. \(400\)
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. \(\left[L^{{-1/2}}T^{{-1/2}}\right]\)
If \(y = a\sin(bt-cx)\), where \(y\) and \(x\) represent length and \(t\) represents time, then which of the following has the same dimensions as that of \(\frac{ab^2}{c}\)?
1. \((\text{speed})^2\)
2. \(\text{momentum}\)
3. \(\text{angle}\)
4. \(\text{acceleration}\)
The universal gravitational constant is dimensionally represented as:
1.
2.
3.
4.
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