A body of mass 5 kg moving with a uniform speed 3√2 ms^-1 in X-Y

Question

A body of mass 5 kg moving with a uniform speed \(3\sqrt2\, ms^{-1}\) in X – Y plane along the line y = x + 4. The angular momentum of the particle about the origin will be ______ kg \(m^2 s^{–1}\)

Answer 1

The angular momentum of the particle about the origin will be 60 kg m² s^–1.

y – x – 4 = 0

\(d_1\) is perpendicular distance of given line from origin

\(d_1 = |\frac{-4}{\sqrt{1^2+1^2}}| \Rightarrow 2\sqrt 2\, m\)

So, \(|\vec L| = mvd_1 = 5 \times 3\sqrt 2 \times 2\sqrt2\, kg \,m^2/s\)

\(= 60\, kg\, m^2/s\)