The unit of thermal conductivity is:
1. | W m–1 K–1 | 2. | J m K–1 |
3. | J m–1 K–1 | 4. | W m K–1 |
In an experiment, the percentage errors that occurred in the measurement of physical quantities \(A,\) \(B,\) \(C,\) and \(D\) are \(1\%\), \(2\%\), \(3\%\), and \(4\%\) respectively. Then, the maximum percentage of error in the measurement of \(X,\) where \(X=\frac{A^2 B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^3}\), will be:
1. \(10\%\)
2. \(\frac{3}{13}\%\)
3. \(16\%\)
4. \(-10\%\)
The velocity \(v\) of a particle at time \(t\) is given by \(v=at+\dfrac{b}{t+c}\), where \(a,\) \(b\) and \(c\) are constants. The dimensions of \(a,\) \(b\) and \(c\) are respectively:
1. \(\left[{LT}^{-2}\right],[{L}] \text { and }[{T}]\)
2. \( {\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]} \)
3. \( {\left[{LT}^2\right],[{LT}] \text { and }[{L}]} \)
4. \( {[{L}],[{LT}] \text { and }\left[{T}^2\right]}\)
Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T, and current I, would be:
1.
2.
3.
4.
1. | \(a=1,\) \(b=-1,\) \(c=-2\) | pressure if
2. | \(a=1,\) \(b=0,\) \(c=-1\) | velocity if
3. | \(a=1,\) \(b=1,\) \(c=-2\) | acceleration if
4. | \(a=0,\) \(b=-1,\) \(c=-2\) | force if
1. | \([Ev^{-2}T^{-1}]\) | 2. | \([Ev^{-1}T^{-2}]\) |
3. | \([Ev^{-2}T^{-2}]\) | 4. | \([E^{-2}v^{-1}T^{-3}]\) |
A student measured the diameter of a small steel ball using a screw gauge of least count \(0.001\) cm. The main scale reading is \(5\) mm and zero of circular scale division coincides with \(25\) divisions above the reference level. If the screw gauge has a zero error of \(-0.004\) cm, the correct diameter of the ball is:
1. | \(0.521\) cm | 2. | \(0.525\) cm |
3. | \(0.053\) cm | 4. | \(0.529\) cm |
The main scale of a vernier callipers reads 10 mm in 10 divisions. 10 divisions of Vernier scale coincide with 9 divisions of the main scale. When the two jaws of the callipers touch each other, the fifth division of the vernier coincides with 9 main scale divisions and the zero of the vernier is to the right of zero of main scale. When a cylinder is tightly placed between the two jaws, the zero of vernier scale lies slightly behind 3.2 cm and the fourth vernier division coincides with a main scale division. The diameter of the cylinder is.
(1) 3.10 cm
(2) 3.8 cm
(3) 3.09 cm
(4) -3.09 cm