question_answer

An object of mass m is projected vertically upwards with a speed of \[{{v}_{0}}\]At the same moment another object of mass M, which is initially above the projected one, is dropped from a height of h. The two point like objects collide completely in elastically, and they stick to each other. Find kinetic energy (in J) of combined mass just before it hits the ground.\[(Given : m = 1 kg, {{v}_{0}}= 20 m/s,\] \[M=3 kg, h=20m,g= 10m/{{s}^{2}})\]

A) 550 J

B) 650 J

C) 450 J

D) 250 J

Correct Answer: B

Solution :

[b] Using relative velocity, time of flight before collision will be \[t=\frac{20}{20}=15\] By COM at the time of collision \[3\times 10-1\times 10=4\times v\] \[2\times 10=4\times v;\,\,5=v\] \[v=5m/s\] For 1-D motion \[{{\operatorname{v}}^{2}}={{u}^{2}}+2as={{5}^{2}}+2\times  10\times 15=25+300=325\]\[K=650\text{ }J\]