The position of a body with acceleration \(a\) is given by \(x= Ka^{m}t^{n}\) (assume \(t\) to be time). The values of \(m\) and \(n\) will be:
1. | \(m=1,~n=1\) | 2. | \(m=1,~n=2\) |
3. | \(m=2,~n=1\) | 4. | \(m=2,~n=2\) |
The period of oscillation of a simple pendulum is given by \(T = 2\pi \sqrt{\frac{l}{g}}\) where \(l\) is about \(100~\text{cm}\) and is known to have \(1~\text{mm}\) accuracy. The period is about \(2~\text{s}\). The time of \(100\) oscillations is measured by a stopwatch of least count \(0.1~\text{s}\). The percentage error in \(g\) is:
1. \(0.1\%\)
2. \(1\%\)
3. \(0.2\%\)
4. \(0.8\%\)
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. | \(1\%\) |
What is the number of significant figures in \(0.310\times 10^{3}?\)
1. | \(2\) | 2. | \(3\) |
3. | \(4\) | 4. | \(6\) |
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 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 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. | \(4\%\) |
In an experiment, the following observations were recorded: initial length \(L =2.820~\text{m}\), mass \(M = 3.00~\text{kg}\), change in length \(l = 0.087~\text{cm}\), diameter \(D = 0.041~\text{cm}\). Taking \(g = 9.81~\text{m/s}^2\) and using the formula, \(Y = \frac{4MgL}{\pi D^2l},\) the maximum permissible error in \(Y \) will be:
1. \(7.96\%\)
2. \(4.56\%\)
3. \(6.50\%\)
4. \(8.42\%\)
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 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. | \(4\) |