A light-year is a unit of:
1. Time
2. Mass
3. Distance
4. Energy
In \(S= a+bt+ct^2,~S\) is measured in metres and \(t\) in seconds. The unit of \(c\) will be:
1. | none | 2. | \(\text{m}\) |
3. | \(\text{ms}^{-1}\) | 4. | \(\text{ms}^{-2}\) |
If \(u_1\) and \(u_2\) are the units selected in two systems of measurement and \(n_1\) and \(n_2\) are their numerical values, then:
1. | \(n_1u_1=n_2u_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) |
2. | \(n_1u_1+n_2u_2=0\) |
3. | \(n_1n_2=u_1u_2\) |
4. | \((n_1+u_1)=(n_2+u_2)\) |
The dimensional formula for impulse is:
1. \([MLT^{-2}]\)
2. \([MLT^{-1}]\)
3. \([ML^2T^{-1}]\)
4. \([M^2LT^{-1}]\)
In the relation, \(y=a \cos (\omega t-k x)\), the dimensional formula for \(k\) will be:
1. \( {\left[M^0 L^{-1} T^{-1}\right]} \)
2. \({\left[M^0 L T^{-1}\right]} \)
3. \( {\left[M^0 L^{-1} T^0\right]} \)
4. \({\left[M^0 L T\right]}\)
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. \(1\%\)
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 cm. Its diameter is measured with vernier callipers having the least count of 0.01 cm. Given that the length is 5.0 cm and the radius is 2.0 cm. The percentage error in the calculated value of the volume will be
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. \(D\)