Hey JayDilla, I get 1/3. Here's how:
Kinetic energy due to linear motion is:

where

giving

The rotational part requires the moment of inertia of a solid cylinder

Then the rotational kinetic energy is

Adding the two types of energy and factoring out common terms gives

Here the "1" in the parenthesis is due to linear motion and the "1/2" is due to the rotational part. Since this gives a total of 3/2 altogether, and the rotational part is due to a third of this (1/2), I say it's 1/3.
Well, the tension in the thread will probably quadruple, but the hanging body will continue to just hang there.
The question gives us no evidence that it is doing any oscillating, and there's no reason for it to start just because it suddenly got heavier.
Answer:
b. 
Explanation:
As we know that the electric field due to infinite line charge is given as

here we can find potential difference between two points using the relation

now we have

now we have

now plug in all values in it


now we know by energy conservation


Answer:
(a) 
(b) 
(c) 
Explanation:
(a) According to Newton's second law, the acceleration of a body is directly proportional to the force exerted on it and inversely proportional to it's mass.

(b) According to Newton's third law, the force that the sled exerts on the girl is equal in magnitude but opposite in the direction of the force that the girl exerts on the sled:

(c) Using the kinematics equation:

For the girl, we have
and
. So:

For the sled, we have
. So:

When they meet, the final positions are the same. So, equaling (1) and (2) and solving for t:

Now, we solve (1) for 
