Answer:
5.4 ms⁻¹
Explanation:
Here we have to use conservation of energy. Initially when the stick is held vertical, its center of mass is at some height above the ground, hence the stick has some gravitational potential energy. As the stick is allowed to fall, its rotates about one. gravitational potential energy of the stick gets converted into rotational kinetic energy.
= length of the meter stick = 1 m
= mass of the meter stick
= angular speed of the meter stick as it hits the floor
= speed of the other end of the stick
we know that, linear speed and angular speed are related as

= height of center of mass of meter stick above the floor = 
= Moment of inertia of the stick about one end
For a stick, momentof inertia about one end has the formula as

Using conservation of energy
Rotational kinetic energy of the stick = gravitational potential energy

Answer:
After 4 s of passing through the intersection, the train travels with 57.6 m/s
Solution:
As per the question:
Suppose the distance to the south of the crossing watching the east bound train be x = 70 m
Also, the east bound travels as a function of time and can be given as:
y(t) = 60t
Now,
To calculate the speed, z(t) of the train as it passes through the intersection:
Since, the road cross at right angles, thus by Pythagoras theorem:


Now, differentiate the above eqn w.r.t 't':


For t = 4 s:

Answer:
ρ = 7500 kg/m³
Explanation:
Given that
mass ,m = 12 kg
Displace volume ,V= 1.6 L
We know that
1000 m ³ = 1 L
Therefore V= 0.0016 m ³
When metal piece is fully submerged
We know that
mass = Density x volume

Now by putting the values in the above equation

ρ = 7500 kg/m³
Therefore the density of the metal piece will be 7500 kg/m³.
Answer: a) 127 eV; b) there is no change of kinetic energy.
Explanation: In order to explain this problem we have to use the change of potentail energy ( conservative field) is equal to changes in kinetic energy. So for the proton ther move to lower potential then they gain kinetic energy from the electric field. This means the electric force do work in this trayectory and then the protons increased changes its speed.
If we replace the proton by a electron we have a very different situaction, the electrons are located in a lower potental then they can not move to higher potential if any external force does work on the system.
In resumem, the electrons do not move from a point with V=87 to other point with V=-40 V. The electric force point to high potential so the electrons can not move to lower potential region (V=-40V).
Answer:
<em>The centripetal acceleration would increase by a factor of 4</em>
<em>Correct choice: B.</em>
Explanation:
<u>Circular Motion</u>
The circular motion is described when an object rotates about a fixed point called center. The distance from the object to the center is the radius. There are other magnitudes in the circular motion like the angular speed, tangent speed, and centripetal acceleration. The formulas are:


If the speed is doubled and the radius is the same, then


The centripetal acceleration would increase by a factor of 4
Correct choice: B.