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Question

A body is falling from a height h. After it has fallen from a height h2, it will possess


A

only potential energy

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B

only kinetic energy

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C

half potential and half kinetic energy

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D

more kinetic and less potential energy

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Solution

The correct option is C

half potential and half kinetic energy


Step 1. Given data

It is given that a body is falling from a height h. After it has fallen from a height h2.

Step 2. Formula to be used

The energy possessed by the body due to virtue of its motion is called Kinetic energy.

The kinetic energy is,

K.E.=12mv2

Here, m is mass, v is velocity and K.E. is kinetic energy.

The energy possessed by a body due to the virtue of its position or configuration is called potential energy.

P.E.=mgh

Here, m is mass, g is gravitational field strength and h is height.

Step 3. Find the energy which possesses by the given height

Let a body of mass ′m′ placed at a height h above the ground, and start falling down from rest which is shown in above figure.
When the body falls from a height h to h2, the potential energy is given as mgh2.
The body covers the distance h2 with a velocity v. We make use of the third equation of motion to obtain the velocity of the body.

According to the third equation of motion is,

v2-u2=2as

Here, v is the velocity at any point in time, u is the initial velocity, a is the acceleration and s is the distance travelled. From the given,

u=0

a=g

s=x

So,

v2-0=2gh2

v2=gh

Now,

Kinetic energy =12mv2

=mgh2

So, at height h2 the energy possessed is half potential energy and half the kinetic energy.

Hence, option C is the correct answer.


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