Question

A student writes an expression for the momentum (p) of a body of mass (m) with total energy (e) and considering the duration of time (t) as p = check its correctness on dimensional analysis.

Answer 1

Answer:

M]=[Mass]=[M0L0T0]

[J]=[Angular momentum]=[ML2T−1]

[L]=[Length]

Now; [ML2T−1]=[M0L0T0]

∴[L2]=[T]

Power [P]=[MLT−2.LT−1]

=[ML2T−3]

=[L2L−6]

[P]=[L−4]

Energy/work [W]=[MLT−2.L]

=[L2L−4]

=[L−2]

Force [F]=[MLT−2]=[L.L−4]=[L−3]

Linear momentum [p]=[MLT−1]=[L.L−2]

[p]=[L−1].