Q1> A particle of mass 'm' was transferred from the center of the base of uniform hemisphere of mass 'M' and radius 'R' into infinity.What work was performed in the process by the gravitational force on the particle by the hemisphere?
Q2> A motor boat going downstream overcame a raft at a point 'A'. After time=60 minutes, it turned back and after some time passed the raft at a distance 6km from point 'A'. Find the flow velocity assuming the duty of the engine to be constant.
Q3> A proton with kinetic energy=10MeV flies past a stationary free electron at a distance 'b'=10pm.Find the energy acquired by the electron , assuming the proton's trajectory to be rectilinear and the electron to be practically motionless as the proton flies by.
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1 Answers
49For question 2:
The words of question 2 were vaguely placed. I changed them a bit for the problem to make some sense.
Let us suppose the river's velocity is u and the motorboat's velocity in still water is v.
Since the raft is a passive device (flows with the water), it's velocity will also be u.
The boat has velocity v+u downstream and -(v-u) upstream.
In the expression -(v-u) the (v-u) part takes care of the magnitude of velocity while the (-) sign signifies it is in opposite direction.
Now, what we can see is, in the frame of reference of the raft, the relative velocity of the boat when it is going downstream is v (v+u - u) and when it is going upstream is -v (-v+u - u).
Thus we can draw the displacement time graph of the motor-boat as seen by the raft.
This will give us an idea of relation between the time for which the boat has travelled downstream and that travelled upstream. (which turn out to be equal).
That was the hint, now give it a try.
