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 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 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. | \(5.4~\text{cm}\) |
1. | \(9.98\) m | 2. | \(9.980\) m |
3. | \(9.9\) m | 4. | \(9.9801\) m |
A screw gauge has the least count of \(0.01~\text{mm}\) 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
If \({x}=\frac{{a} \sin \theta+{b} \cos \theta}{{a}+{b}},\) then:
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 thin wire has a length of \(21.7~\text{cm}\) and a radius of \(0.46~\text{mm}\). The volume of the wire to correct significant figures is:
1. | \( 0.15~ \text{cm}^3 \) | 2. | \( 0.1443~ \text{cm}^3 \) |
3. | \( 0.14~ \text{cm}^3 \) | 4. | \( 0.144 ~\text{cm}^3\) |
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 \(\dfrac{ab^2}{c}?\)
1. \((\text{speed})^2\)
2. \(\text{momentum}\)
3. \(\text{angle}\)
4. \(\text{acceleration}\)