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 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. \(m=2,~n=2\)

"Pascal-Second" has dimension of 

1. Force

2. Energy

3. Pressure

4. Coefficient of viscosity

In a system of units if force (F), acceleration (A) and time (T) are taken as fundamental units then the dimensional formula of energy is 

1. FA²T

2. FAT²

3. F²AT

4. FAT

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: