The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of

1. Frequency

2. Velocity

3. Angular momentum

4. Time

Which of the following group have different dimensions?

1. Potential difference, EMF, voltage

2. Pressure, stress, young's modulus

3. Heat, energy, work-done

4. Dipole moment, electric flux, electric field

Out of the following four-dimensional quantities, which one quantity is to be called a dimensional constant?

1. Acceleration due to gravity

2. Surface tension of water

3. Weight of a standard kilogram mass

4. The velocity of light in a vacuum

The density of a liquid in the CGS system is 0.625 g/cm³. What is its magnitude in the SI system?

1. 0.625

2. 0.0625

3. 0.00625

4. 625

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:

What is the number of significant figures in \(0.310\times 10^{3}?\)

Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is 

1. 1%

2. 3%

3. 5%

4. 7%

The mean time period of second's pendulum is 2.00s and mean absolute error in the time period is 0.05s. To express maximum estimate of error, the time period should be written as

1. (2.00 ± 0.01) s

2. (2.00 + 0.025) s

3. (2.00 ± 0.05) s

4. (2.00 ± 0.10) s

A body travels uniformly a distance of (13.8 $\pm$ 0.2) m in a time (4.0 ± 0.3) sec. The velocity of the body within error limits is:

1. (3.45 ± 0.2) ms^-1

2. (3.45 ± 0.3) ms^-1

3. (3.45 ± 0.4) ms^-1

4. (3.45 ± 0.5) ms^-1