If the units of force and length, is increased by four times, then the unit of energy increases by:
1. | \(16\) times | 2. | \(8\) times |
3. | \(2\) times | 4. | \(4\) times |
The velocity \(v\) of a particle at time \(t\) is given by \({v}={at}+\frac{{b}}{{t}+{c}}.\) The dimensions of \({a}\), \({b}\), and \({c}\) are respectively:
1. \( {\left[{LT}^{-2}\right],[{L}],[{T}]} \)
2. \( {\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]} \)
3. \( {\left[{LT}^2\right],[{LT}] \text { and }[{L}]} \)
4. \( {[{L}],[{LT}], \text { and }\left[{T}^2\right]}\)
If \(97.52\) is divided by \(2.54\), the correct result in terms of significant figures is:
1. | \( 38.4 \) | 2. | \(38.3937 \) |
3. | \( 38.394 \) | 4. | \(38.39\) |
A physical quantity \(A\) is related to four observable quantities \(a\), \(b\), \(c\) and \(d\) as follows, \(A= \frac{a^2b^3}{c\sqrt{d}},\) the percentage errors of measurement in \(a\), \(b\), \(c\) and \(d\) are \(1\%\), \(3\%\), \(2\%\) and \(2\%\) respectively. The percentage error in quantity \(A\) will be:
1. \(12\%\)
2. \(7\%\)
3. \(5\%\)
4. \(14\%\)
The number of significant figures in the numbers \(25.12,\) \(2009,\) \(4.156\) and \(1.217\times 10^{-4}\) is:
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
A physical quantity \(P\) is given by \(P=\dfrac{A^3 B^{1/2}}{C^{-4}D^{3/2}}.\) The quantity which contributes the maximum percentage error in \(P\) is:
1. \(A\)
2. \(B\)
3. \(C\)
4. \(D\)
The length of a cylinder is measured with a meter rod having the least count of \(0.1~\text{cm}\). Its diameter is measured with vernier callipers having the least count of \(0.01~\text{cm}\). Given that the length is \(5.0~\text{cm}\) and the radius is \(2.0~\text{cm}\). The percentage error in the calculated value of the volume will be:
1. \(1\%\)
2. \(2\%\)
3. \(3\%\)
4. \(4\%\)
The periods of oscillation of a simple pendulum in an experiment are recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s, and 2.80 s respectively. The average absolute error will be:
1. 0.1 s
2. 0.11 s
3. 0.01 s
4. 1.0 s
The decimal equivalent of \(\frac{1}{20} \) up to three significant figures is:
1. | \(0.0500\) | 2. | \(0.05000\) |
3. | \(0.0050\) | 4. | \(5.0 \times 10^{-2}\) |
The percentage errors in the measurement of mass and speed are \(2\%\) and \(3\%\) respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed:
1. \(11\%\)
2. \(8\%\)
3. \(5\%\)
4. \(1\%\)