the total length of te string ist taken to be constant as the string is light and in extensible the height of the pullys are taken from the same potential level and divided as the total lenght of the string and differentiated

FOR BETTER UNDERSTANDING CONSULT ENGINEERING DYNAMICS BY MARRIAM AND  KRAIGE

FROM THERE LEARN FIRST AND SECOND DEGREE OF FREEDOM

YOUR CONCEPT WILL DEFINITELY BE CLEARED TRUST ME

Well I am not an expert

A my brother is an iitian I could give you some advice

IN PHYSICS

Try to think more rather than solving problems from Irodov and other books try to solve a single problems in different ways give time and effort to learn simple things believe me learning simple things is very important it boosts the basic. No matter how brilliant you are if you don't have grip over the subject you can't crack the iit The questions in the iit are from the basics of the subject so understanding as without the basics you can't do harder problems

IF YOU ARE ASKING ME HOW MANY HOURS A DAY YOU HAVE TO STUDY WELL THEN  THE EFFORT YOU PUT IN YOURWORK DESIDES THAT TIME IS NOT THE FACTOR UNDERSTANDING IS?

TMH and Arihant are good

Physics

HCVerma

Irodov

SS Krotov (Problems in Physics)

AKSingh (Problems in Physics)

resnik and halliday

Chemistry

Arihant (New pattern IIT Chemistry) 

morisson boyd

Atkins

Advanced Inorganic Chemistry (Cotton and Wilkinson) [better than JDLee]

mtg chemistry today

Mathematics

I A Maron

MLKhanna

TMH

If u dont mind I will suggest u all should take a look at problem in physics by Abhay Kumar Singh, problems in physics by Zubov and Shalnov

even though there is friction it doesnot play any role in pure rolling in only comes into play when there is rolling with slipping. To determine the direction of friction

There is no answer

the options where

1 mgtanalpha

2 0

3 Frition will bring about shifting the normal reaction from the ground but it actual value cant be said

4 none of these

Horse Power was defined as the raise in height of a bucket of water form a well by a healthy english horse in 45 minutes