1. **Rolling Question :**

A sphere S rolls without slipping mving with a constant speed on a plank P.The friction between the upper surface of P and the sphere is sufficient to prevent slipping , while the lower surface of P is smooth and rests on the ground.Initially ,P is fixed to the ground by a pin N.If N is suddenly removed :

[A] S will begin to slip on P

[B] P will begin to move backwards

[C] The speed of S will decrease and its angular velocity will increase

[D] There will be no change in the motion of S and P will still be at rest.

Answer given : [D] !

**IMPORTANT POINT / DOUBT : I just cant understand where the reaction (of the friction force on the sphere) acting on P vanishes , why is it not able to make P move ??? [7]**

2.**Extremely BASIC question from Waves** [I'm poor at Mechanics :( ]

A string of length L is stretched by L /10 and the velocity of transverse wave along it is v .When it is stretched by L/20 [assuming Hooke's Law is applicable ] , the velocity of wave will become :

[A] v

[B] √2 v

[C] v√2

[D] 2v

Answer given : [C ]

**IMPORTANT POINT / DOUBT : This answer will come if we use the relation v is directly proportional to √T [ T: Tension , v: velocity] and then proceeding by Hooke's law..BUT how can we say that v is directly proportional to √T when length of the medium changes ?? [7]**

3.**ANOTHER DOWN TO EARTH BASIC QUESTION from Laws of Motion : **

In the figure given below ,the spring ,the pulleys and the strings are all massless.The pulleys are frictionless at their axles and it is given that m_{1}> 2m_{2}.The system is initially in equilibrium and the string connecting m_{2} to the rigid support below is now cut.The initial acceleration of m_{2} immediately after cutting the string will be :

Figure :

[A] (m_{1}-2m_{2)}2m_{2} g

[B] (m_{1}-m_{2)}m_{2} g

[C] (2m_{1}-m_{2)}m_{2} g

[D] (m_{2}-m_{1)}m_{2} g

Answer given : [A]

**MY DOUBT: HOW ?..PLEASE GIVE FULL STEPS..PLEALSE !**