Live practice

The atomic number Z gives protons and A - Z gives neutrons.

Take a \(100\,\mathrm{g}\) sample, convert each element's mass into moles, and reduce the mole ratio to the smallest whole numbers.

Principle and reasoning. Work from the governing physical relation and apply it to every stated part.

Use v=sqrt(T/μ) after finding linear mass density.

Principle and reasoning. Work from the governing physical relation and apply it to every stated part.

Thermal equilibrium is fixed by equality of heat lost and gained. The heat capacity of each body determines its temperature change.

Principle and reasoning. Work from the governing physical relation and apply it to every stated part.

Use proportional intervals on the straight calibration line.

Twice the orbital rate means half the period. Apply Kepler's third law.

Impulse equals change in momentum and therefore has direction.

There is no external horizontal force. Hence total horizontal momentum and centre-of-mass velocity remain constant.

Define the sample space and count each favourable outcome once.

The final value lies in [0,1]; complement pairs also sum to one, providing an independent check.

Form the required totals explicitly and divide by the full number of observations.

The variance is nonnegative and the reported standard deviation is its positive square root.