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Total energy = kinetic energy (KE) + potential energy(PE)
KE > 0 since m and v2 is positive. If KE <0 particles cannot be find. If PE>TE, then KE<0 (now in all graph check for this condition)
In case 1 kinetic energy is negative for x<a. So at x<a particle cannot be found.
In case 2 for x<a and for x> b kinetic energy is negative. So the particle cannot be found in these regions.
In the...

By Einstein’s mass-energy relation we can write :
Here and C are constant thus two-body decay is unable to explain (or account for) the continuous energy distribution in the β-decay of a neutron.

The potential energy of the system depends inversely on the separation between the balls. Thus the potential energy will decrease as the balls will come closer and will become zero as they touch each other.
Thus elastic collision is best described only by the graph (v).

The initial momentum of the system (boy + trolley) is given as :
Now assume v' is the final velocity of the trolley with respect to the ground.
Then the final momentum will be :
Conserving momentum :
...

In this case, the heat produced is the loss in the potential energy.
Thus,
heat produced = mg h
or
or
The heat produced (when the lift is stationary) will remain the same as the relative velocity of the bolt with respect lift still remains zero.

Displacement (x) of the block is given as : = 0.1 m.
Using equilibrium conditions we can write :
and ( is the frictional force).
We can write work done in terms of potential energy as :
or ...

The FBD of the track is shown in the figure below :
Using the law of conservation of energy we have :
or
Hence both stones will reach the bottom with the same speed.
For stone 1 we can write :
or ...

We are given :
Mass of the bullet m: 0.012 Kg
Mass of the block M: 0.4 Kg
The initial velocity of the bullet u: 70 m/s
The initial velocity of the block : 0
The final velocity of the system (bullet + block): v
For finding the final speed of system we will apply the law of conservation of momentum :
or ...

A typical has dimensions of .
The area of the roof of the house is .
This is nearly equal to the area required for the production of the given amount of electricity.

It is given that the efficiency of energy conversion is 20 per cent.
According to question, we can write (equating power used by family) :
(Here A is the area required.)
or
or
Thus required area is 200 m2.

Efficiency is given to be 20 per cent.
Thus energy supplied by the person :
Thus the amount of fat lost is :
or

The work done against the gravitational force is given by :
= Number of times the weight is lifted work done in 1 time.
or
or

It is given that 25 per cent of wind energy is converted into electrical energy.
Thus electric energy produced is :
or
Now the electric power is given by :
or
or ...

The volume of wind = here is the swept circle and is the velocity.
Thus the mass of the wind is : - , is the density of the air.
Hence mass of wind flowing through windmill in time t is .

The relation between work done and the kinetic energy is given by :
Using the relation we can write :
Initial velocity = 0 (at x = 0 )
And the final velocity = (at x = 2).
Thus work done is :
or
or ...

Since the sand is falling in the trolley thus the force generated on the system (trolley and sandbag) is an internal force. There is no external force thus momentum of the system doesn't change. Hence speed remains the same i.e., 27 Km/hr.

Consider the extreme position (horizintal) :-
The kinetic energy at this position is zero as velocity is zero.
Thus total energy is given by :
Now consider the mean position (lowermost point) :
Here the potential energy of bob is zero.
Whereas kinetic energy is :
...

Mass of the water is :
or
Thus the output power is given by :
or
or
or
Also, we are given...

This is an elastic collision thus the transfer of momentum will take place. It is given that bob B is at rest and bob A has some velocity. So in momentum transfer, bob B will gain the velocity in the left direction whereas bob A will come to rest (complete momentum transfer takes place).
Hence bob A will not rise.

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