question_answer

(a) Two masses one n times heavier than the other are dropped from same height. How do their momentum compare just before they hit the ground? (b) Two masses one n times heavy as the other have equal kinetic energy. How do their momentum compare?                

Answer:

                (a) When dropped from same height, the two masses hit the ground with same velocity=\[\sqrt{2gh}\] \[\therefore \]                  \[\frac{{{p}_{2}}}{{{p}_{1}}}=\frac{{{m}_{2}}}{{{m}_{1}}}=n\] (b) We know that K.E. \[K=\frac{{{p}^{2}}}{2m}\]                              \[\therefore \]\[\text{p}=\sqrt{2mK}\] As K is same, \[\frac{{{p}_{2}}}{{{p}_{1}}}=\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}=\sqrt{n}\]