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. \(\text{acceleration}\)