Hi pitchu !!!
First of all let me tell you that Pitchu is a very cool an cute name !!!!
Now, lets get back to business !!! For the questions i have not been able to make free body diagrams. Sorry, but i will try to explain with the best of my ability.
Q. 7) Here, consider ma . Here, forces acting on it are :-
1. Force F2 exerted by the experimenter.
2. Force F exerted by block mb.
As the block accelerates, F2 - F = maa [ where a=acceleration ]
Now, consider mb . Here, forces are :-
1. Force F exerted by block mb . This is because Force
exerted by both blocks on each other is 0 due to
action-reaction pair.
As, this block accelerates with same acceleration,
F = mba
Solve both the equations i.e
F2 - mba = maa
F2 = a ( ma+mb )
instead of a you can put F / mb [ Eq. 2 ]
So, you get = F2 = F ( 1 + ma/mb )
Q. 9) Look,
Here,
use v2 = u2 + 2as
v = 0 [ as drops come to rest ]
u = 30 m/s [ Velocity of drops before hitting the head ]
s = 0.001 m [ Distance covered by each drop ]
So,
By solving this we get the retardation[as drops retard],
a = 450000 m/s2 fsdfsf
So, force provided by each drop = ma
= 4*10-6 * 450000 N
= 1.8 N
Q.12) Look,
Here,
Let the force exerted by each friend be F. This is equal to the tension
in each string. Let that tension be T
Now, at any height, the ropes make an equal angle p with the
vertical.
Wen you break the components for the tensions by making
free body diagram for the person in the "khadda", you get
2Tcosp = mg
As, the friends pull him slowly the acceleration can be assumed to be
0.
T = mg/2cosp
Now, mg is constant
As, the person comes up, p increases.
If, p increases cosp decreases.
So, T increases.
i.e first part proved.
At a height h, [ please see the diagram ]
cosp = h / [h^2 + (d/2)^2 ]^2
T = mg / 2cosp
Solve it and you get the answer as given in the book.